problem solving volume cylinder

Volume of Cylinders

A cylinder is a solid with two congruent circles joined by a curved surface.

In the above figure, the radius of the circular base is r and the height is h.

The volume of the cylinder is the area of the base × height. Since the base is a circle and the area of a circle is πr 2 then the volume of the cylinder is πr 2 × h.

Volume of cylinder = πr 2 h

Surface Area of cylinder = 2πr 2 + 2πrh

Calculate the volume of a cylinder where:

a) the area of the base is 30 cm 2 and the height is 6 cm. b) the radius of the base is 14 cm and the height is 10 cm.

Sometimes you may be required to calculate the volume of a hollow cylinder or tube or pipe.

Volume of hollow cylinder: = πR 2 h – πr 2 h = πh (R 2 – r 2 )

The figure shows a section of a metal pipe. Given the internal radius of the pipe is 2 cm, the external radius is 2.4 cm and the length of the pipe is 10 cm. Find the volume of the metal used.

Solution: The cross section of the pipe is a ring: Area of ring = [ π (2.4) 2 – π (2) 2 ]= 1.76 π cm 2

These videos show how to solve word problems about cylinders.

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Cylinder Volume Calculator

How to calculate volume of a cylinder, volume of a hollow cylinder, volume of an oblique cylinder.

Our cylinder volume calculator enables calculating the volume of that solid. Whether you want to figure out how much water fits in a can, coffee in your favorite mug, or even the volume of a drinking straw – you're in the right place. The other option is calculating the volume of a cylindrical shell (hollow cylinder).

Let's start from the beginning – what is a cylinder? It's a solid bounded by a cylindrical surface and two parallel planes. We can imagine it as a solid physical tin having lids on top and bottom. To calculate its volume, we need to know two parameters – the radius (or diameter) and height:

cylinder volume = π × cylinder radius² × cylinder height

The cylinder volume calculator helps in finding the volume of right, hollow and oblique cylinders:

The hollow cylinder, also called the cylindrical shell, is a three-dimensional region bounded by two right circular cylinders having the same axis and two parallel annular bases perpendicular to the cylinders' common axis.

It's easier to understand that definition by imagining, e.g., a drinking straw or a pipe – the hollow cylinder is this plastic, metal, or other material. The formula behind the volume of a hollow cylinder is:

cylinder_volume = π × (R² - r²) × cylinder_height

where R – external radius, and r – internal radius

Similarly, we can calculate the cylinder volume using the external diameter, D , and internal diameter, d , of a hollow cylinder with this formula:

cylinder_volume = π × [(D² - d²)/4] × cylinder_height

To calculate the volume of a cylindrical shell, let's take some real-life examples, maybe... a roll of toilet paper, because why not? 😀

Enter the external diameter of the cylinder . The standard is equal to approximately 11 cm.

Determine the internal cylinder diameter . It's the internal diameter of the cardboard part, around 4 cm.

Find out what's the height of the cylinder ; for us, it's 9 cm.

Tadaaam! The volume of a hollow cylinder is equal to 742.2 cm³.

Remember that the result is the volume of the paper and the cardboard. If you want to calculate how much plasticine you can put inside the cardboard roll, use the standard formula for the volume of a cylinder – the calculator will calculate it in the blink of an eye!

The oblique cylinder is the one that 'leans over' – the sides are not perpendicular to the bases in contrast to a standard 'right cylinder'. How to calculate the volume of an oblique cylinder? The formula is the same as for the straight one. Just remember that the height must be perpendicular to the bases.

Now that you know how to calculate a volume of a cylinder, maybe you want to determine the volumes of other 3D solids? Use this general volume calculator !

If you are curious about how many teaspoons or cups fit into your container, use our volume converter .

To calculate the volume of soil needed for flower pots of different shapes – also for the cylindrical one – use the potting soil calculator .

Where can you find cylinders in nature?

Cylinders are all around us , and we are not just talking about Pringles’ cans. Although things in nature are rarely perfect cylinders, some examples are tree trunks & plant stems, some bones (and therefore bodies), and the flagella of microscopic organisms. These make up a large amount of the natural objects on Earth!

How do you draw a cylinder?

To draw a cylinder, follow these steps:

Draw a slightly flattened circle. The more flattened it is, the closer you are to looking at the cylinder side on .

Draw two equal, parallel lines from the far sides of your circle going down.

Link the ends of the two lines with a semi-circular line that looks the same as the bottom half of your top circle.

Add shadow and shading as appropriate.

How do you calculate the weight of a cylinder?

To calculate the weight of a cylinder:

Square the radius of the cylinder .

Multiply the square of radius by pi and the cylinder’s height .

Multiply the volume by the density of the cylinder. The result is the cylinder’s weight.

How do you calculate the surface area to volume ratio of a cylinder?

Find the volume of the cylinder using the formula πr²h .

Find the surface area of the cylinder using the formula 2πrh + 2πr² .

Make a ratio out of the two formulas, i.e., πr²h : 2πrh + 2πr² .

Alternatively, simplify it to rh : 2(h+r) .

Divide both sides by one of the sides to get the ratio in its simplest form.

How do you find the height of a cylinder?

If you have the volume and radius of the cylinder:

• Make sure the volume and radius are in the same units (e.g., cm³ and cm).

Square the radius.

• Divide the volume by the radius squared and pi to get the height in the same units as the radius.

If you have the surface area and radius (r):

• Make sure the surface and radius are in the same units .
• Subtract 2πr² from the surface area.
• Divide the result of step 2 by 2πr.
• The result is the height of the cylinder.

How do I find the radius of a cylinder?

If you have the volume and height of the cylinder:

• Make sure the volume and height are in the same units (e.g., cm³ and cm).
• Divide the volume by pi and the height.
• Square root the result.

If you have the surface area and height (h):

• Substitute the height, h, and surface area into the equation, surface area = 2πrh + 2πr².
• Divide both sides by 2π.
• Subtract surface area/2π from both sides.
• Solve the resulting quadratic equation.
• The positive root is the radius.

How do you find the volume of an oval cylinder?

To find the volume of an oval cylinder:

Multiply the smallest radius of the oval (minor axis) by its largest radius (major axis).

Multiply this new number by pi .

Divide the result of step 2 by 4. The result is the area of the oval.

Multiply the area of the oval by the height of the cylinder.

The result is the volume of an oval cylinder.

How do you find the volume of a slanted cylinder?

To calculator the volume of a slanted cylinder:

Find the radius, side length, and slant angle of the cylinder.

Multiply the result by pi.

Take the sin of the angle .

Multiply the sin by the side length.

Multiply the result from steps 3 and 5 together.

The result is the slanted volume.

How do you calculate the swept volume of a cylinder?

To compute the swept volume of a cylinder:

Divide the bore diameter by 2 to get the bore radius .

Square the bore radius.

Multiply the square radius by pi.

Multiply the result of step 3 by the length of the stroke . Make sure the units for bore and stroke length are the same.

The result is the swept volume of one cylinder.

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Formula Volume of a Cylinder

How to find the Volume of a Cylinder

This page examines the properties of a right circular cylinder . A cylinder has a radius (r) and a height (h) (see picture below).

Cylinder Volume Formula

Practice Problems on Area of a Cylinder

What is the volume of the cylinder with a radius of 2 and a height of 6?

Use the formula for the volume of a cylinder as shown below.

• Volume = Π *(r) 2 (h)
• Volume = Π *(2) 2 (6)

What is the volume of the cylinder with a radius of 3 and a height of 5?

• Volume = Π *(3) 2 (5)

What is the area of the cylinder with a radius of 6 and a height of 7?

Use the area of a cylinder formula .

• Volume = Π *(6) 2 (7)

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Volume of Cylinder

The volume of a cylinder is the capacity of the cylinder which calculates the amount of material quantity it can hold. In geometry, there is a specific formula to calculate the volume of a cylinder that is used to measure how much amount of any quantity whether liquid or solid can be immersed in it uniformly. A cylinder is a three-dimensional shape with two congruent and parallel identical bases. There are different types of cylinders. They are:

• Right circular cylinder: A cylinder whose bases are circles and each line segment that is a part of the lateral curved surface is perpendicular to the bases.
• Oblique Cylinder: A cylinder whose sides lean over the base at an angle that is not equal to a right angle.
• Elliptic Cylinder: A cylinder whose bases are ellipses.
• Right circular hollow cylinder: A cylinder that consists of two right circular cylinders bounded one inside the other.

The formula to find the volume of a cylinder is V = πr 2 h. Let us learn more about this formula in the upcoming sections.

What is the Volume of a Cylinder?

The volume of a cylinder is the number of unit cubes (cubes of unit length) that can be fit into it. It is the space occupied by the cylinder as the volume of any three-dimensional shape is the space occupied by it. The volume of a cylinder is measured in cubic units such as cm 3 , m 3 , in 3 , etc. Let us see the formula used to calculate the volume of a cylinder.

Definition of a Cylinder

A cylinder is a three-dimensional solid shape that consists of two parallel bases linked by a curved surface. These bases are like a circular disk in a shape . The line passing from the center or joining the centers of two circular bases is called the axis of the cylinder.

Volume of Cylinder Formula

We know that a cylinder resembles a prism (but note that a cylinder is not a prism as it has a curved side face), we use the same formula of volume of a prism to calculate the volume of a cylinder as well. We know that the volume of a prism is calculated using the formula,

V = A × h, where

• A = area of the base

Using this formula, the formulas of volume of cylinder are:

• The formula for volume of a right circular cylinder is, V = πr 2 h (r = radius, h = height)
• The formula for volume of an oblique cylinder is, V = πr 2 h (r = radius, h = height)
• The formula for volume of an elliptic cylinder is, V = πabh (a and b = radii, h = height)
• The formula for volume of a right circular hollow cylinder is, V = π(R 2 - r 2 )h (R = outer radius, r = inner radius, h = height)

Now we will apply the formula V = A × h to calculate the volume of different types of cylinders.

Volume of a Right Circular Cylinder Formula

We know that the base of a right circular cylinder is a circle and the area of a circle of radius 'r' is πr 2 . Thus, the volume (V) of a right circular cylinder, using the above formula (V = A × h), is,

• 'r' is the radius of the base (circle) of the cylinder
• 'h' is the height of the cylinder
• π is a constant whose value is either 22/7 (or) 3.142.

Thus, the volume of cylinder directly varies with its height and directly varies with the square of its radius. i.e., if the radius of the cylinder becomes double, then its volume becomes four times.

Formula to Find Volume of an Oblique Cylinder

The formula to calculate the volume of cylinder (oblique) is the same as that of a right circular cylinder. Thus, the volume (V) of an oblique cylinder whose base radius is 'r' and whose height is 'h' is,

Formula to Calculate Volume of an Elliptic Cylinder

We know that an ellipse has two radii. Also, we know that the area of an ellipse whose radii are 'a' and 'b' is πab. Thus, the volume of an elliptic cylinder is,

• 'a' and 'b' are the radii of the base (ellipse) of the cylinder.
• 'h' is the height of the cylinder.

Volume of a Right Circular Hollow Cylinder Formula

As a right circular hollow cylinder is a cylinder that consists of two right circular cylinders bounded one inside the other, its volume is obtained by subtracting the volume of the inside cylinder from that of the outside cylinder. Thus, the volume (V) of a right circular hollow cylinder is,

V = π(R 2 - r 2 )h

• 'R' is the base radius of the outside cylinder.
• 'r' is the base radius of the inside cylinder.
• π is a constant whose value is 22/7 (or) 3.142.

How To Find the Volume of Cylinder?

Here are the steps to find the volume of cylinder:

• Identify the radius to be 'r' and height to be 'h' and make sure that they both are of the same units.
• Substitute the values in the volume formula V = πr 2 h.
• Write the units as cubic units.

Example: Find the volume of a right circular cylinder of radius 50 cm and height 1 meter. Use π = 3.142.

The radius of the cylinder is, r = 50 cm.

Its height is, h = 1 meter = 100 cm.

Its volume is, V = πr 2 h = (3.142)(50) 2 (100) = 785,500 cm 3 .

Note: We need to use the formula to find the volume of a cylinder depending on its type as we discussed in the previous section. Also, assume that a cylinder is a right circular cylinder if there is no type given and apply the volume of a cylinder formula to be V = πr 2 h.

Important Notes on Volume of Cylinder:

• The volume of a cylinder is calculated using the formula, V = πr 2 h, where r is the radius of its circular base and 'h' is the perpendicular distance (height) between the centres of the bases.
• If diameter (d) is given, then find the radius (r) using r = d/2 and then substitute in the above formula to find the volume of cylinder.

Volume of Cylinder Examples

Example 1: Find the volume of a cylindrical water tank in litres whose base radius is 25 m and whose height is 120 m. Use π = 3.14.

The radius of the cylindrical tank is, r = 25 m.

Its height is, h = 120 m.

Using the formula of volume of cylinder, the volume of the tank is,

V = (3.14)(25) 2 (120) = 235500 cubic meters.

The volume of a cylinder in litres is obtained by using the conversion formula 1 cubic meter = 1000 liters.

Thus, the volume of the tank in liters is: 235500 × 1000 = 235,500,000

Answer: The volume of the given cylindrical tank is 235,500,000 liters.

Example 2: Calculate the volume of an elliptic cylinder whose base radii are 7 inches and 10 inches, and whose height is 15 inches. Use π = 22/7.

The base radii of the given elliptic cylinder are,

a = 7 inches and b = 10 inches.

Its height is, h = 15 inches.

Using the volume of cylinder formula, the volume of the given elliptic cylinder is,

V = (22/7) × 7 × 10 × 15 = 3300 cubic inches.

Answer: The volume of the given cylinder is 3,300 cubic inches.

Example 3: What is the volume of the cylinder with a radius of 4 units and a height of 6 units?

Since the exact type of cylinder is not mentioned, we need to assume it is a right circular cylinder.

Radius,r = 4 units and height,h = 6 units

Volume of the cylinder, V = πr 2 h cubic units.

V = (22/7) × (4) 2 × 6 V = 22/7 × 16 × 6

V= 301.71 cubic units.

Answer: The volume of the cylinder is 301.71 cubic units.

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Practice Questions on Volume of Cylinder

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FAQs on Volume of Cylinder

What is the meaning of volume of cylinder.

The volume of a cylinder is the amount of space in it. It can be obtained by multiplying its base area by its height. The formula to find the  volume of a cylinder of base radius 'r' and height 'h' is V = πr 2 h.

What Is the Formula for Calculating the Volume of a Cylinder?

The formula for calculating the volume of a cylinder is V = πr 2 h, where

• 'r' is the radius of the base of the cylinder
• π is a constant whose value is equal to approximately 3.142.

What is the Volume of a Cylinder with Diameter?

Let us consider a cylinder of radius 'r', diameter 'd', and height 'h'. The volume of a cylinder of base radius 'r' and height 'h' is V = πr 2 h. We know that r = d/2. By substituting this in the above formula, V = πd 2 h/4.

What Is the Ratio of the Volume of a Cylinder and a Cone?

Let us consider a cylinder and a cone , each with base radius 'r' and height 'h'. We know that the volume of the cylinder is πr 2 h and the volume of the cone is 1/3 πr 2 h. Thus the required ratio is 1:(1/3) (or) 3:1.

How To Calculate Volume of a Cylinder With Diameter and Height?

The volume of a cylinder with base radius 'r' and height 'h' is, V = πr 2 h. If its base diameter is d, then we have d = r/2. Substituting this in the above formula, we get V = πd 2 h/4. Thus, the formula to find the volume of a cylinder with the diameter (d) and height(h) is V = πd 2 h/4.

How To Find Volume of Cylinder With Circumference and Height?

We know that the circumference of a circle of radius 'r' is C = 2πr. Thus, when the circumference of the base of a cylinder (C) and its height (h) are given, then we first solve the equation C = 2πr for 'r' and then we apply the volume of a cylinder formula, which is, V = πr 2 h.

How To Calculate Volume of Cylinder in Litres?

We can use the following conversion formulas to convert the volume of cylinder from m 3 (or) cm 3 to liters.

• 1 m 3 = 1000 liters
• 1 cm 3 = 1 ml (or) 0.001 liters
• Metric Conversion
• Unit Conversion

What Happens to the Volume of Cylinder When Its Radius Is Halved?

The volume of cylinder varies directly with the square of its radius. Thus, when its radius is halved, the volume becomes 1/4 th .

What Happens to the Volume of Cylinder When Its Radius Is Doubled?

We know that the volume of cylinder is directly proportional to the square of its radius. Thus, when its radius is doubled, the volume becomes four times.

How Do You Find Volume of Cylinder Using Calculator?

Volume of a cylinder calculator is a machine to calculate a cylinder's volume. To calculate the volume of a cylinder using a calculator we need to provide necessary inputs to the calculator tool, such as required dimensions like radius, diameter, height, etc. Try now the volume of a cylinder calculator enter the radius and height of the cylinder in the given box of the volume of a cylinder calculator. Click on the "Calculate" button to find the volume of a cylinder. By clicking the "Reset" button you can easily clear the previously entered data and find the volume of a cylinder for different values.

☛Also Check:

• Cylinder Calculator
• Surface Area of Cylinder Calculator
• Height of a Cylinder Calculator

What is the Area and Volume of a Cylinder?

The surface area of a cylinder is the total area or region covered by the surface of the cylinder. The surface area of a cylinder is given by two following formulas:

• The curved surface area of cylinder = 2πrh
• The total surface area of the cylinder = 2πr 2 +2πrh = 2πr(h+r)

The area of a cylinder is expressed in square units, like m 2 , in 2 , cm 2 , yd 2 , etc.

The volume of a cylinder is the total amount of capacity immersed in a cylinder that can be calculated using the volume of cylinder equation is V = πr 2 h and it is measured in cubic units.

• Surface Area of Cylinder Worksheets
• Volume of a Cylinder Worksheets
• Surface Area Formulas

How Does the Volume of a Hollow Cylinder Change When the Height is Doubled?

The volume of a hollow cylinder formula is V = π(R 2 - r 2 )h cubic units. According to the volume formula, we can see that volume is directly proportional to the height of the hollow cylinder. Therefore, the volume gets doubled when the height of the hollow cylinder is doubled.

What is the Volume of Cylinder in Terms of Pi?

The volume of cylinder is defined as the capacity of a cylinder which is indicated in terms of pi. The volume of a cylinder in terms of pi is expressed in cubic units where units can be m 3 , cm 3 , in 3 , ft 3 , etc.

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Volume Of A Cylinder

Here we will learn about the volume of a cylinder, including how to calculate the volume of a cylinder given its radius and perpendicular height.

There are also cylinder worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.

What is the volume of a cylinder?

The volume of a cylinder is the amount of space there is inside a cylinder. 

In order to find the volume of a cylinder we first need to find the circular area of the base.

The formula for calculating the area of a circle is:

We then multiply the area of the circular base by the height (or length) of the cylinder.

The formula for the volume of a cylinder is:

Where r is the radius of a cylinder and h is the perpendicular height of a cylinder.

Find the volume of this cylinder with radius of the base 7 cm and perpendicular height 10 cm .

How to calculate the volume of a cylinder

In order to calculate the volume of a cylinder:

• Write down the formula: \text{Volume}=\pi r^2 h

Substitute the given values.

Work out the calculation.

Write the final answer, including units.

Volume of a cylinder worksheet

Get your free volume of a cylinder worksheet of 20+ questions and answers. Includes reasoning and applied questions.

Volume of a cylinder examples

Example 1: volume of a cylinder.

Find the volume of the cylinder with radius 3 cm and perpendicular height 5 cm .  

Give your answer to 1 decimal place.

Write down the formula.

To answer the question we need the formula for the volume of a cylinder.

2 Substitute the given values.

We need to substitute the value of the radius r and the perpendicular height h into the formula.

3 Work out the calculation.

You may need to work out volumes with of without a calculator. A calculator can be used to work out the decimal answer.

4 Write the final answer, including units.

Check what form the final answer needs to be.

You may need to leave your answer in terms of \pi or as a decimal with rounding. Here we are asked to give the answer to 1 decimal place.

The volume of the cylinder is: 141.4 cm^{3} (to 1 dp)

Example 2: volume of a cylinder

Find the volume of the cylinder with radius 4.8 cm and perpendicular height 7.9 cm .

Give your answer to 3 significant figures.

For this question you can use a calculator to work out the volume.

You may need to leave your answer in terms of \pi or as a decimal with rounding.

Here we are asked to give the answer to 3 significant figures.

The volume of the cylinder is: 572 cm^{3} (to 3 sf)

Example 3: volume of a cylinder

Find the volume of the cylinder with radius 3 cm and perpendicular height 7 cm . 

Leave your answer in terms of \pi .

Work out the volume (focusing on the number parts of the calculation).

The volume of the cylinder is: 63 cm^{3}

Example 4: volume of a cylinder

Find the volume of the cylinder with radius 4 cm and perpendicular height 10 cm . 

The volume of the cylinder is: 160\pi cm^{3}

Example 5: using the formula to find a length

The volume of a cylinder is 1600 cm^{3} .

Its radius is 9 cm .

Find its perpendicular height.

Give your answer to 2 decimal places.

We need to rearrange the formula to find the value of h .

Here we are asked to give the answer to 2 decimal places.

The perpendicular height of the cylinder is: 6.29 cm (to 2 dp)

Example 6: using the formula to find a length

The volume of a cylinder is 1400 cm^{3} .

Its perpendicular height is 15 cm .

Find its radius.

The radius of the cylinder is: 5.45 cm (to 2 dp)

Common misconceptions

It is important to not round the answer until the end of the calculation. This will mean your final answer is accurate.

• Using the radius or the diameter

It is a common error to mix up radius and diameter. Remember the radius is half of the diameter and the diameter is double the radius.

• Correc t units

For area we use square units such as cm^2 .

For volume we use cube units such as cm^3 .

Related lessons

Volume of a cylinder is part of our series of lessons to support revision on rounding numbers. You may find it helpful to start with the main cylinder lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:

• Surface area of a cylinder

Practice volume of a cylinder questions

1. Find the volume of a cylinder with a radius 3.2 cm and perpendicular height 9.1 cm.

We are finding the volume of a cylinder so we substitute the value of r and h into the formula.

2. Find the volume of a cylinder with a radius 5.3 cm and perpendicular height 3.8 cm .

3. Find the volume of a cylinder with a radius 8 cm and perpendicular height 7 cm .

4. Find the volume of a cylinder with a radius 4 cm and perpendicular height 8 cm .

5. The volume of a cylinder is 250 cm^3 .

Its radius is 2.9 cm .

Using the formula we substitute the value of the volume and the value of the radius and rearrange to find the radius.

6. The volume of a cylinder is 800 cm^3 .

Its perpendicular height is 9.2 cm .

Using the formula we substitute the value of the volume and the value of the perpendicular height and rearrange to find the radius.

Volume of a cylinder GCSE questions

1. Here is a cylinder.

Calculate the volume of the cylinder.

\pi \times 5.3^2 \times 4.7 For substituting the radius and the perpendicular height into the formula

414.762…=415 For the correct answer

2. Here is a cylinder.

\pi \times 3^2 \times 8 For substituting the radius and the perpendicular height into the formula

72\pi For the correct answer

3. This diagram shows a container.

The container is in the shape of a cylinder. The container is empty.

Nina has a bucket. She is going to use the bucket to fill the container with water.

The bucket holds 8 litres of water. How many buckets of water are needed to fill the container?

( 1 litre = 1000 cm^2 )

\pi \times 25^2 \times 80 For using the formula to find the volume of the container

157 079.63… For the correct volume

157 079.63… \div 8000 For dividing the volume of the container by the volume of the buckets with the same units

=19.63… = 20 buckets For the correct number of buckets

Learning checklist

You have now learned how to:

• Work out the volume of a cylinder
• Solve problems involving the volume of a cylinder

The next lessons are

• Surface area of a cuboid
• Surface area of a sphere

Beyond GCSE

For GCSE we look at right circular cylinders – where the bases are parallel planes and the height is perpendicular to these bases. It is possible to have oblique cylinders.

It is also possible to have a cylinder with an ellipse as its cross-section.

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Volume of a Cylinder

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A cylinder is a right circular prism. It is a solid object with 2 identical flat circular ends, and a curved rectangular side. Like other prisms, the volume can be obtained by multiplying height by base area.

Consider a cylinder with base radius \(r\) and height \(h\), as shown in the figure above. Since the area of the base is \(\pi r^2\), the volume is equal to \(\pi r^2 h\).

Note: Sometimes, the definition of cylinders may not require having a circular base. In such cases, the base shape will need to be given. The above definition is then called a circular cylinder.

What is the volume of a cylinder with base radius 2 and height 3? The volume is \( \pi \times 2^2 \times 3 = 12 \pi \). \( _\square \)

A cylinder has a volume of \(100\pi\) and a height of \(4\). What is the radius of its base? Let \(r\) denote the radius of the base. Then we have \[\pi r^2\times4=100\pi\Rightarrow r^2=25\Rightarrow r=5.\ _\square \]

If we make a cylinder two times taller, and lengthen its base radius by three-fold, how many times larger would it become in volume? Let \(r\) denote the initial base radius and \(h\) denote the initial height of the cylinder. Then its initial volume is \(V=\pi r^2h\). The problem states that the cylinder's new base radius is \(r'=3r\), and new height is \(h'=2h\). Hence the final volume is \(V'=\pi r'^2h'=\pi\times(3r)^2\times2h=18\pi r^2h\). Therefore the answer is 18 times. \(_\square\)

A container contains a total \(50\pi\text{ m}^3\) of water. If we are to distribute this water into cylindrical cups of base radius \(0.5\text{ m}\) and height \(1\text{ m}\), how many cups do we need? The volume of each cylindrical cup is \( \pi \times 0.5^2 \times 1 = 0.25 \pi\text{ m}^3 \). Therefore the number of cups we need is \(\frac{50\pi}{0.25\pi}=200.\) \( _\square \)

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Volume of a Cylinder Calculator

Use this cylinder volume calculator to easily calculate the volume of a cylinder from its base radius and height in any metric: mm, cm, meters, km, inches, feet, yards, miles...

    Calculation results

Related calculators.

• Volume of a cylinder formula
• How to calculate the volume of a cylinder?
• Example: find the volume of a cylinder
• Practical applications

    Volume of a cylinder formula

The formula for the volume of a cylinder is height x π x (diameter / 2) 2 , where (diameter / 2) is the radius of the base (d = 2 x r), so another way to write it is height x π x radius 2 . Visual in the figure below:

First, measure the diameter of the base (usually easier than measuring the radius), then measure the height of the cylinder. To do the calculation properly, you must have the two measurements in the same length units. The result from our volume of a cylinder calculator is always in cubic units, based on the input unit: in 3 , ft 3 , yd 3 , cm 3 , m 3 , km 3 , and so on.

    How to calculate the volume of a cylinder?

One can think of a cylinder as a series of circles stacked one upon another. The height of the cylinder gives us the depth of stacking, while the area of the base gives us the area of each circular slice. Multiplying the area of the slice by the depth of the stack is an easy way to conceptualize the way for calculating the volume of a cylinder. Since in practical situations it is easier to measure the diameter (of a tube, a round steel bar, a cable, etc.) than it is to measure the radius, and on most technical schemes it is the diameter which is given, our cylinder volume calculator accepts the diameter as an input. If you have the radius instead, just multiply it by two.

Using the formula and doing the calculations by hand can be difficult due to the value of the π constant: ~3.14159, which can be hard to work with, so a volume of a cylinder calculator significantly simplifies the task.

    Example: find the volume of a cylinder

Applying the volume formulas is easy provided the cylinder height is known and one of the following is also given: the radius, the diameter, or the area of the base. For example, if the height and area are given to be 5 feet and 20 square feet, the volume is just a multiplication of the two: 5 x 20 = 100 cubic feet.

If the radius is given, using the second equation above can give us the cylinder volume with a few additional steps. For example, the height is 10 inches and the radius is 2 inches. First, we find the area by 3.14159 x 2 2 = 3.14159 x 4 = 12.574, then multiply that by 10 to get 125.74 cubic inches of volume. Using a higher level of precision for π results in more accurate results, e.g. our calculator computes the volume of this cylinder as 125.6637 cu in.

    Practical applications

The cylinder is one of the most widely used body shapes in engineering and architecture: from tunnels, covered walkways to tubes, cables, round bars, the cylinders and pistons in your car's engine - cylinders are everywhere. Calculating cylinder volume is useful when you want to know its displacement, or how much liquid or gas you need to fill it, e.g. how much water you need to fill your jacuzzi. Cylindrical aquariums are also fairly common, so are cylindrical artificial lakes, fountains, gas containers / tanks, etc.

Cite this calculator & page

If you'd like to cite this online calculator resource and information as provided on the page, you can use the following citation: Georgiev G.Z., "Volume of a Cylinder Calculator" , [online] Available at: https://www.gigacalculator.com/calculators/volume-of-cylinder-calculator.php URL [Accessed Date: 30 Apr, 2024].

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• Volume of Cylinders – Explanation & Examples

Volume of Cylinders – Explanation & Examples

This article will show you how to find the volume of a cylinder by using cylinder volume formula.

In geometry, a cylinder is a 3-dimensional shape with two equal, and parallel circles joined by a curved surface.

The distance between the circular faces of a cylinder is known as the height of a cylinder . The top and bottom of a cylinder are two congruent circles whose radius or diameter are denoted as ‘ r ’ and ‘ d ’, respectively.

How to Find the Volume of a Cylinder?

To calculate the volume of a cylinder, you need the radius or diameter of the circular base or top and a cylinder’s height.

The volume of a cylinder is equal to the product of the area of the circular base and the height of the cylinder. The volume of a cylinder is measured in cubic units.

Calculation of the volume of a cylinder is useful when designing cylindrical objects such as:

• Cylindrical water tanks or wells
• Perfume or chemical bottles
• Cylindrical containers and pipes
• Cylindrical flasks used in chemistry labs

Cylinder volume formula

The formula for the volume of a cylinder is given as:

Volume of a cylinder = πr 2 h cubic units

Where πr 2 = area of a circle;

r = radius of the circular base and;

h = height of a cylinder.

For a hollow cylinder, the volume formula is given as:

Volume of a cylinder = πh (r 1 2  – r 2 2 )

Where, r 1  = external radius and r 2 = internal radius of a cylinder.

The difference of the external and internal radius forms the wall thickness of a cylinder i.e.

Wall thickness of a cylinder = r 1 – r 2

Let’s solve a few example problems about the volume of cylinders.

The diameter and height of a cylinder are 28 cm and 10 cm, respectively. What is the volume of the cylinder?

The radius is half of the diameter.

Diameter = 28 cm ⇒ radius = 28/2

Height = 10 cm

By the cylinder volume formula;

volume = πr 2 h

= 3.14 x 14 x 14 x 10

= 6154.4 cm 3

So, the volume of the cylinder is 6154.4 cm 3

The depth of water in a cylindrical tank is 8 feet. Suppose the radius and height of the tank are 5 feet and 11.5 feet, respectively. Find the volume of water required to fill the tank to the brim.

First calculate the volume of the cylindrical tank

Volume = 3.14 x 5 x 5 x 11.5

= 902.75 cubic feet

Volume of water in the tank = 3.14 x 5 x 5 x 8

= 628 cubic feet.

The volume of water required to fill the tank = 902.75 – 628 cubic feet

= 274.75 cubic feet.

The volume of a cylinder is 440 m 3 , and the radius of the base is 2 m. Calculate the height of the tank.

Volume of a cylinder = πr 2 h

440 m 3 = 3.14 x 2 x 2 x h

440 = 12.56h

By dividing 12.56 on both sides, we get

Therefore, the height of the tank is 35 meters.

The radius and height of a cylindrical water tank are 10 cm and 14 cm, respectively. Find the volume of the tank in liters.

= 3.14 x 10 x 10 x 14

= 4396 cm 3

Given, 1 Liter = 1000 cubic centimeter (cm 3 )

Therefore, divide 4396 by 1000 to get

Volume = 4.396 liters

The external radius of a plastic pipe is 240 mm, and the internal radius is 200 mm. If the pipe’s length is 100 mm, find the volume of material used to make the pipe.

A pipe is an example of a hollow cylinder, so we have

= 3.14 x 100 x (240 2 – 200 2 )

= 3.14 x 100 x 17600

= 5.5264 x 10 6 mm 3 .

A cylindrical solid block of a metal is to be melted to form cubes of edge 20 mm. Suppose the radius and length of the cylindrical block are 100 mm and 490 mm, respectively. Find the number of cubes to be formed.

Calculate the volume of the cylindrical block

volume = 3.14 x 100 x 100 x 490

= 1.5386 x 10 7 mm 3

Volume of the cube = 20 x 20 x 20

= 8000 mm 3

The number of cubes = volume of the cylindrical block/volume of the cube

= 1.5386 x 10 7 mm 3 / 8000 mm 3

= 1923 cubes.

Find the radius of a cylinder with the same height and volume as a cube of sides 4 ft.

Height of cube = height of cylinder = 4 feet and,

volume of the cube = volume of cylinder

4 x 4 x 4 = 64 cubic feet

But volume of a cylinder = πr 2 h

3.14 x r 2 x 4 = 64 cubic feet

12.56r 2 =64

Divide both sides by 12.56

r 2 = 5.1 feet.

Therefore, the radius of the cylinder will be 1.72 feet.

A solid hexagonal prism has a base length of 5 cm and a height of 12 cm. Find the height of a cylinder with the same volume as the prism. Take the radius of the cylinder to be 5 cm.

The formula for the volume of a prism is given as;

Volume of a prism = (h)(n) (s 2 )/ [4 tan (180/n)]

where, n = number of sides

s = base length of a prism

h = height of a prism

Volume = (12) (6) (5 2 )/ (4tan 180/6)

=1800/2.3094

=779.42 cm 3

779.42 =3.14 x 5 x 5 x h

h = 9.93 cm.

So, the height of the cylinder will be 9.93 cm.

Practice Questions

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• Math Article
• Volume Of A Cylinder

Volume of a Cylinder

The volume of a cylinder is the density of the cylinder which signifies the amount of material it can carry or how much amount of any material can be immersed in it. Cylinder’s volume is given by the formula,  πr 2 h, where r is the radius of the circular base and h is the height of the cylinder. The material could be a liquid quantity or any substance which can be filled in the cylinder uniformly. Check volume of shapes here.

Volume of cylinder has been explained in this article briefly along with solved examples for better understanding. In Mathematics , geometry is an important branch where we learn the shapes and their properties. Volume and surface area are the two important properties of any 3d shape.

The cylinder is a three-dimensional shape having a circular base. A cylinder can be seen as a set of circular disks that are stacked on one another. Now, think of a scenario where we need to calculate the amount of sugar that can be accommodated in a cylindrical box.

In other words, we mean to calculate the capacity or volume of this box. The capacity of a cylindrical box is basically equal to the volume of the cylinder involved. Thus, the volume of a three-dimensional shape is equal to the amount of space occupied by that shape.

Volume of a Cylinder Formula

A cylinder can be seen as a collection of multiple congruent disks, stacked one above the other. In order to calculate the space occupied by a cylinder, we calculate the space occupied by each disk and then add them up. Thus, the volume of the cylinder can be given by the product of the area of base and height.

For any cylinder with base radius ‘r’, and height ‘h’, the volume will be base times the height.

Therefore, the cylinder’s volume of base radius ‘r’, and height ‘h’ = (area of base) × height of the cylinder

Since the  base is the circle, it can be written as

Volume =  πr 2  × h

Therefore, the volume of a cylinder = πr 2 h cubic units.

Volume of Hollow Cylinder

In case of hollow cylinder, we measure two radius, one for inner circle and one for outer circle formed by the base of hollow cylinder. Suppose, r 1 and r 2  are the two radii of the given hollow cylinder with ‘h’ as the height, then the volume of this cylinder can be written as;

• V =  πh(r 1 2 – r 2 2 )

Surface Area of Cylinder

The amount of square units required to cover the surface of the cylinder is the surface area of the cylinder. The formula for the surface area of the cylinder is equal to the total surface area of the bases of the cylinder and surface area of its sides.

• A = 2πr 2 + 2πrh

Volume of Cylinder in Litres

When we find the volume of the cylinder in cubic centimetres, we can convert the value in litres by knowing the below conversion, i.e.,

1 Litre = 1000 cubic cm or cm 3 For example: If a cylindrical tube has a volume of 12 litres, then we can write the volume of the tube as 12 × 1000 cm 3 = 12,000 cm 3

Question 1: Calculate the volume of a given cylinder having height 20 cm and base radius of 14 cm. (Take pi = 22/7)

Height  = 20 cm

radius = 14 cm

we know that;

Volume, V = πr 2 h  cubic units

V=(22/7) × 14  × 14  × 20

V= 12320 cm 3

Therefore, the volume of a cylinder = 12320 cm 3

Question 2: Calculate the radius of the base of a cylindrical container of volume 440 cm 3 . Height of the cylindrical container is 35 cm. (Take pi = 22/7)

Volume = 440 cm 3

Height = 35 cm

We know from the formula of cylinder;

So, 440 =  (22/7) × r 2  × 35

r 2  = (440  × 7)/(22 × 35) = 3080/770 = 4

Therefore, r = 2 cm

Therefore, the radius of a cylinder = 2 cm.

Related Links

Frequently asked questions on volume of a cylinder, what is meant by the volume of a cylinder.

In geometry, the volume of a cylinder is defined as the capacity of the cylinder, which helps to find the amount of material that the cylinder can hold.

What is the formula for the volume of a cylinder?

The formula to calculate volume of a cylinder is given by the product of base area and its height. Since, the base area of a cylinder is circular, we can state that Volume of a cylinder = πr 2 h cubic units.

What is the volume of a hollow cylinder?

As we know, the hollow cylinder is a type of cylinder, which is empty from inside and it should possess some difference between the internal and the external radius. Thus, the amount of space occupied by the hollow cylinder in the three dimensional space is called the volume of a hollow cylinder.

How to calculate the volume of a hollow cylinder?

If R is the external radius and r is the internal radius, then the formula for calculating the cylinder’s volume is given by: V = π (R 2 – r 2 ) h cubic units.

What is the unit for the volume of a cylinder?

The volume of a cylinder is generally measured in cubic units, such as cubic centimeters (cm 3 ), cubic meters (m 3 ), cubic feet (ft 3 ) and so on.

How to find the volume of a cylinder if the diameter and height are given?

As we know, Diameter “d” = 2(Radius) = 2r. So, r = d/2 Now, substitute the value of “r” in the volume of cylinder formula, we get V = πr 2 h = π(d/2) 2 h V = (πd 2 h)/4 Hence, the volume of the cylinder is (πd 2 h)/4, if its diameter and height are given.

What will happen to the cylinder’s volume if its radius is doubled?

As we know, cylinder’s volume is directly proportional to the square of its radius. If the radius is doubled, (i.e., r = 2r), we get V = πr 2 h =π(2r) 2 h = 4πr 2 h. Hence, the cylinder’s volume becomes four times, when its radius is doubled.

What will happen to the cylinder’s volume if its radius is halved?

We know that, the volume of cylinder ∝ Radius2 Thus, if radius is halved, (i.e., r = r/2), we get V = π(r/2) 2 h = (πr 2 h)/4 Therefore, the cylinder’s volume becomes 1/4th, if its radius is halved.

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Volume Worksheets

This humongous collection of printable volume worksheets is sure to walk middle and high school students step-by-step through a variety of exercises beginning with counting cubes, moving on to finding the volume of solid shapes such as cubes, cones, rectangular and triangular prisms and pyramids, cylinders, spheres and hemispheres, L-blocks, and mixed shapes. Brimming with learning and backed by application the PDFs offer varied levels of difficulty.

List of Volume Worksheets

Counting Cubes

• Volume of Cubes
• Volume of Rectangular Prisms
• Volume of Triangular Prisms

Volume of Mixed Prisms

• Volume of Cones
• Volume of Cylinders

Volume of Spheres and Hemispheres

• Volume of Rectangular Pyramids
• Volume of Triangular Pyramids

Volume of Mixed Pyramids

Volume of Mixed Shapes

Volume of Composite Shapes

Explore the Volume Worksheets in Detail

Work on the skill of finding volume with this batch of counting cubes worksheets. Count unit cubes to determine the volume of rectangular prisms and solid blocks, draw prisms on isometric dot paper and much more.

Volume of a Cube

Augment practice with this unit of pdf worksheets on finding the volume of a cube comprising problems presented as shapes and in the word format with side length measures involving integers, decimals and fractions.

Volume of a Rectangular Prism

This batch of volume worksheets provides a great way to learn and perfect skills in finding the volume of rectangular prisms with dimensions expressed in varied forms, find the volume of L-blocks, missing measure and more.

Volume of a Triangular Prism

Encourage students to work out the entire collection of printable worksheets on computing the volume of triangular prism using the area of the cross-section or the base and leg measures and practice unit conversions too.

Navigate through this collection of volume of mixed prism worksheets featuring triangular, rectangular, trapezoidal and polygonal prisms. Bolster practice with easy and moderate levels classified based on the number range used.

Volume of a Cone

Motivate learners to use the volume of a cone formula efficiently in the easy level, find the radius in the moderate level and convert units in the difficult level, solve for volume using slant height, and find the volume of a conical frustum too.

Volume of a Cylinder

Access our volume of a cylinder worksheets to practice finding the radius from diameter, finding the volume of cylinders with parameters in integers and decimals, find the missing parameters, solve word problems and more!

Take the hassle out of finding the volume of spheres and hemispheres with this compilation of pdf worksheets. Gain immense practice with a wide range of exercises involving integers and decimals.

Volume of a Rectangular Pyramid

This exercise is bound to help learners work on the skill of finding the volume of rectangular pyramids with dimensions expressed as integers, decimals and fractions in easy and moderate levels.

Volume of a Triangular Pyramid

Help children further their practice with this bundle of pdf worksheets on determining the volume of triangular pyramids using the measures of the base area or height and base. The problems are offered as 3D shapes and in word format in varied levels of difficulty.

Gain ample practice in finding the volume of pyramids with triangular, rectangular and polygonal base faces presented in two levels of difficulty. Apply relevant formulas to find the volume using the base area or the other dimensions provided.

Upscale practice with an enormous collection of printable worksheets on finding the volume of solid shapes like prisms, cylinders, cones, pyramids and revision exercises to revisit concepts with ease.

Learn to find the volume of composite shapes that are a combination of two or more solid 3D shapes. Begin with counting squares, find the volume of L -blocks, and compound shapes by adding or subtracting volumes of decomposed shapes.

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Lesson Solved problems on volume of cylinders

VOLUME OF CYLINDERS SPHERES AND CONES WORD PROBLEMS

(1)  Find the volume of a solid cylinder whose radius is 14 cm and height is 30 cm.

(2)  A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, then find the quantity of soup to be prepared daily in the hospital to serve 250 patients?

(3)   The sum of the base radius and the height of a solid cylinder is 37 cm. If the total surface area of the cylinder is 1628 sq.cm, then find the volume of the cylinder.

(4)  Volume of a solid cylinder is 62.37 cu.cm. Find the radius if its height is 4.5 cm.

(5)   The radii of two right circular cylinders are in the ratio 2:3. Find the ratio of their volumes if their heights are in the ratio 5:3.

(6)  The radius and height of two circular cylinders are in the ratio 5 : 7. If its volume is 4400 cu.cm, find the radius of the cylinder.

(7)   A rectangular sheet of metal foil with dimension 66 cm x 12 cm is rolled to form a cylinder of height 12 cm. Find the volume of the cylinder.

(8)   A lead pencil is in the shape of right circular cylinder. The pencil is 28 cm long and its radius is 3 mm. If the lead is of radius 1 mm, then find the volume of the wood used in the pencil.

(9)  Radius and slant height of a cone are 20 cm and 29 cm respectively. Find its volume.

(10)  The circumference of the base of a 12 m high wooden solid cone is 44 m. Find the volume.

(11)  A vessel is in the form of frustum of a cone. Its radius at one end and the height are 8 cm and 14 cm respectively. If its volume is 5676/3 cm 3 , then find the radius at the other end.

(12)  The perimeter of the ends of a frustum of a cone are 44 cm and 8.4 Π cm. If the depth is 14 cm, then find its volume.

(13)  A right angled triangle ABC with sides 5 cm, 12 cm and 13 cm is revolved about the fixed side of 12 cm. Find the volume of the solid generated.

(14)  The radius and height of a right circular cone are in the ratio 2:3. Find the slant height if its volume is 100.48 cu.cm (take Π = 3.14).

(15)  The volume of a cone with circular base is 216 Π cu.cm. If the base radius is 9 cm, then find the height of the cone.

(16)  Find the mass of 200 steel spherical ball bearings, each of which has radius 0.7 cm, given that the density of steel is 7.95 g/cm 3 . (Mass = Volume x Density).

(17)  The outer and inner radii of a hollow sphere are 12 cm and 10 cm. Find its volume.

(18)  The volume of a solid hemisphere is 1152 Π cu.cm. Find its curved surface area.

(19)  Find the volume of the largest right circular cone that can be cut of a cube whose edge is 14 cm.

(20)  The radius of a spherical balloon increase from 7 cm to 14 cm as air is being pumped into it. Find the ratio of volumes of the balloon in the two cases.

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Title: finite volume simulation of a semi-linear neumann problem (keller-segel model) on rectangular domains.

Abstract: In this study, the finite volume method is implemented for solving the problem of the semilinear equation: $-d \delta u+ u=u^q (d, q>0) $with a homogeneous Neumann boundary condition. This problem is equivalent to the known stationary Keller-Segel model, which arises in chemotaxis.After discretization, a nonlinear algebraic system is obtained and solved on the platform Matlab. As a result, many single peaked and multi-peaked shapes in 3D and contour plots can be drawn depending on the parameters d and q.

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Despite a fortified border, migrants will keep coming, analysts agree. Here's why.

Sergio Martínez-Beltrán

Border Patrol picks up a group of people seeking asylum from an aid camp near Sasabe, Arizona, on Wednesday, March 13, 2024. Justin Hamel/Bloomberg via Getty Images hide caption

Border Patrol picks up a group of people seeking asylum from an aid camp near Sasabe, Arizona, on Wednesday, March 13, 2024.

The U.S. southern border is as fortified as ever and Texas is carrying out its own enforcement to stop people from crossing illegally, yet observers and analysts agree on this: migrants not only will continue to come, but their numbers will likely increase in the coming months.

The expected surge can be attributed not only to seasonal migration patterns, but an increase of people displaced by war, poverty, and climate factors in all continents.

And why do these analysts say this?

They keep a close eye on the Darién Gap in Panama and the borders between Central American countries, two key points to gauge the number of people venturing up north.

"In most countries (outward) migration has increased ... particularly in Venezuela, and that's not really reflected yet in the U.S. numbers," said Adam Isacson, an analyst of border and migration patterns at the Washington Office on Latin America, a nonpartisan research and advocacy organization based in Washington D.C.

Despite Mexico's cracking down on migrants, Isacson said people are still making their way up north, even if they need to pause for months at different points during their journey.

"There must be a huge number of people from Venezuela bottled up in Mexico right now," he said.

The Darién Gap serves as a good barometer for migration flows.

This 100-mile-long tropical jungle between Colombia and Panama has claimed the lives of hundreds of migrants, according to a report from the Migration Policy Institute, a Washington, D.C.-based think tank.

Yet the dangers at this jungle are not a deterrent, said Ariel Ruiz Soto, a senior policy analyst with this organization. The majority of people migrating are from Venezuela.

"The reason why I referred to Venezuelans in particular is because they represent a key challenge for removals from Mexico and from the United States to Venezuela," Ruiz Soto said.

Mexico and the U.S. had been flying Venezuelan migrants back to the South American country . However, earlier this year, Venezuelan President Nicolás Maduro stopped accepting flights from the U.S. in response to economic sanctions imposed by the Biden administration.

Panama reported a 2% increase in crossings through the Darién Gap in February compared to the previous month.

Aerial view showing migrants walking through the jungle near Bajo Chiquito village, the first border control of the Darien Province in Panama, on September 22, 2023. LUIS ACOSTA/AFP via Getty Images hide caption

Aerial view showing migrants walking through the jungle near Bajo Chiquito village, the first border control of the Darien Province in Panama, on September 22, 2023.

What the numbers show

Analysts are projecting the increase in the remaining months of the fiscal year, even though U.S. Customs and Border Protection reported a 2.2% decrease in encounters with migrants along the Southern border in March. An encounter is every time a migrant is picked up by immigration authorities.

These numbers are consistent with cyclical patterns of illegal crossings that dip in the winter months, followed by more migrants attempting to get to the U.S. as warm weather arrives, said Ruiz Soto.

In a statement, CBP Spokesperson Erin Waters said the agency remains vigilant to "continually shifting migration patterns" amid "historic global migration."

Waters said the agency has also been partnering with Mexico to curb the flow of people migrating to the U.S.

Mexico has commissioned its National Guard to patrol its borders with Guatemala and the U.S.

"CBP continues to work with our partners throughout the hemisphere, including the Government of Mexico, and around the world to disrupt the criminal networks who take advantage of and profit from vulnerable migrants," Waters said.

Where are migrants crossing the border?

For the last few months, more migrants are attempting to cross through Arizona instead of Texas, according to CBP.

In 2023, the El Paso and Del Rio sector in Texas saw more crossings than any other place across the 2,000-mile Southern border. But this year the Tucson sector in Arizona has seen a 167% increase in crossings, more than any other.

Tiffany Burrow, operations director at Val Verde Border Humanitarian Coalition, an assistance organization for newly border crossers in Del Rio, said she has seen the shift.

"It's empty," Burrow said, pointing to her organizations' office. "There are no migrants."

In March, she helped only three migrants after they were released by CBP pending their court date. In December, they helped 13,511 migrants.

Burrow said that's how migration works — it ebbs and flows.

"We have to be ready to adapt," Burrow said.

Texas Department of Safety Troopers patrol on the Rio Grande along the U.S.-Mexico border. Eric Gay/AP hide caption

Texas Department of Safety Troopers patrol on the Rio Grande along the U.S.-Mexico border.

Texas' role

Burrow and other immigrant advocates are closely observing Texas' ramping up of border enforcement.

In 2021 Gov. Greg Abbott launched Operation Lone Star initiative and deployed the Texas National Guard. Last year the state started lining up razor wire in sections of the Rio Grande.

Texas is also asking the courts to be allowed to implement a law passed last year by the Republican-controlled legislature, known as SB4, which requires local and state police to arrest migrants they suspect are in the country illegally.

It might be too early to know if all these efforts will have an impact on migration patterns, analysts said, considering that Texas saw the highest number of illegal crossings last year.

But, Mike Banks, special advisor on border matters to Abbott, said the state's efforts are fruitful.

Texas has spent over $11 billion in this initiative.

"The vast majority of the United States' southern border is in Texas, and because of Texas' efforts to secure the border, more migrants are moving west to illegally cross the border into other states," said Mike Banks in a statement to NPR.

Ruiz Soto, from the Migrant Policy Institute, said the impact of Texas' policies on arrivals "is likely to be minimal over the long term."

Carla Angulo-Pasel, an assistant professor who specializes in border studies and international migration at the University of Texas at Rio Grande Valley, said that even with Texas' policies in place, migrants are likely to continue to cross.

"You can't claim, as much as I think Gov. Abbott wants to claim, that Operation Lone Star is going to somehow mean that you're going to see less numbers in Texas because that hasn't held true," Angulo-Pasel said. "We could also argue that things are going to progressively get more and more as the spring months progress."