Mathwarehouse Logo

Circles Mixed Exercises

Area, circumference, diameter and radius

Area and circumference both relate to the radius and diameter of a circle. Once you know one, you can find all of the others -- It just takes a little math!

Practice Problems

If a circle's diameter is 10, calculate its circumference and area ?

Circumference = Π×diameter = 10 Π

radius = diameter ÷ 2 = 10 ÷ 2 = 5

A circle's area is 16Π. What is its circumference ?

direction arrow

Circumference = 2Π × radius = 2Π × 4 = 8Π

If a circle has a circumference of 26Π, what is its area .

Area = Π(radius)² = Π(13)² = 169Π

Interesting Fact about Circumference and Area

area of circle through triangle demo

More interesting math facts here !

Ultimate Math Solver (Free) Free Algebra Solver ... type anything in there!

Popular pages @ mathwarehouse.com.

Surface area of a Cylinder

  • Math Article
  • Problems On Circles

Problems On Area And Circumference Of A Circle

Class Registration Banner

Before looking at problems on a circle based on perimeter and area, we need to understand the meaning of a circle and both the properties of the circle. In geometry, a circle is a closed two-dimensional figure in which the set of all the points in the plane is equidistant from a given point called the centre. Let’s have a look the definitions of perimeter and area given below:

Perimeter Definition

Perimeter is associated with any closed figure like triangle , quadrilateral, polygons or circles. It is the measure of distance covered while going around the closed figure on its boundary.

For example, the perimeter of a square of side 2 cm = 8 cm, as we know that the square comprises 4 sides having equal lengths, thus the total distance covered will be 4×2, which will be the total length (i.e. perimeter).

Area Definition

Area means the actual space enclosed by a closed figure (or within the perimeter), and it means all the points within the closed figure and not the boundary.

Perimeter and Area of Circle Formula

Now, coming to the perimeter of a circle, as explained above, is the measure of distance going around the circle’s boundary. This distance is difficult to calculate precisely, and it is easy to visualize that the distance to go around is larger in a larger radius than a smaller radius. Hence, the perimeter is a function of the radius of a circle. In the case of the circle, we generally use the term “CIRCUMFERENCE” instead of the perimeter.

It is given by,

Circumference = 2πr

Here, r is a radius, and π is a constant defined as the ratio of circumference to the circle’s diameter.

The value of π is 22/7 or 3.1416

Also check: Circumference of a circle

The formula to find the area of a circle is given as:

Solved Problems on Circle

Let us understand the concepts related to circles along with the following questions-

To cover a distance of 10 km, a wheel rotates 5000 times. Find the radius of the wheel.

Number of rotations = 5000.

Total distance covered = 10 km

Let ‘r’ be the radius of the wheel.

Circumference of the wheel = Distance covered in 1 rotation = 2πr.

In 5000 rotations, the distance covered = 10 km = 1000000 cm.

\(\begin{array}{l}\text{Hence, in 1 rotation, the distance covered = }\frac{1000000}{5000}cm=200\: cm\end{array} \)

But this is equal to the circumference. Hence, 2πr = 200 cm

Taking the approximate value of π as 22/7, we get

r = 100 x 7/22

r = 31.82 cm approx.

The diameter of a semicircular shape is 14 cm. What will be the perimeter of this shape?

Diameter of semicircle = d = 14 cm

Radius = r = d/2 = 14/2 = 7 cm

Perimeter of semicircle = (Perimeter of circle/2) + d

= (2πr/2) + d

= (22/7) × 7 + 14

The difference between the circumference and the diameter of a circular bangle is 5 cm. Find the radius of the bangle. (Take π = 22/7)

Solution: Let the radius of the bangle be ’r’

According to the question:

Circumference – Diameter=5 cm

We know, Circumference of a circle = 2πr

Diameter of a circle = 2r

Therefore, 2πr – 2r =5 cm

2r(π-1) = 5 cm

\(\begin{array}{l}2r(\frac{22}{7}-1)=5cm\\ \\ 2r\times \frac{15}{7}=5\\ \\ r=\frac{5\times 7}{15\times 2}\\ \\ r=1.166cm\end{array} \)

The radius of bangle is 1.166 cm.

A girl wants to make a square-shaped figure from a circular wire of radius 49 cm. Determine the sides of a square.

Solution: Let the radius of the circle be ’r’.

Length of the wire=circumference of the circle= 2πr

\(\begin{array}{l}= 2\times \frac{22}{7}\times 49=2\times 22\times 7\\ \\ =308\: cm\end{array} \)

Let the side of the square be ‘s’.

Perimeter of the square = length of the wire = 4s

\(\begin{array}{l}s=\frac{308}{4}\\ \\ s=77\:cm\end{array} \)

Therefore, the sides of the square is 77 cm.

Find the area of a circular region whose radius is 21 m.

Radius of circular region = r = 21 m

Area of a circle = πr 2

= (22/7) × 21 × 21

= 22 × 3 × 21

= 1386 sq. m

Therefore, the area of the circular region is 1386 sq. m.

Video Lessons on Circles

Introduction to circles.

problem solving involving circumference of a circle

Parts of a Circle

problem solving involving circumference of a circle

Area of a Circle

problem solving involving circumference of a circle

All about Circles

problem solving involving circumference of a circle

Learn more about Surface area & volumes of the figures with BYJU’S-The learning app.

Leave a Comment Cancel reply

Your Mobile number and Email id will not be published. Required fields are marked *

Request OTP on Voice Call

Post My Comment

problem solving involving circumference of a circle

Register with BYJU'S & Download Free PDFs

Register with byju's & watch live videos.

IMAGES

  1. How to Solve the circumference of a circle « Math :: WonderHowTo

    problem solving involving circumference of a circle

  2. Perimeter of a Circle

    problem solving involving circumference of a circle

  3. Circumference and Area of a Circle Worksheet

    problem solving involving circumference of a circle

  4. Area and Circumference of Circles Word Problems Worksheet and TASK CARDS

    problem solving involving circumference of a circle

  5. How to Solve Problem Involving Circumference of a Circle-Math 5 Q3 W9

    problem solving involving circumference of a circle

  6. 8.5 Solve Problems Involving Circumference of a Circle Diagram

    problem solving involving circumference of a circle

VIDEO

  1. GCSE Maths

  2. Circumference of a Circle

  3. How to Calculate Circumference of a Circle (Step by Step)

  4. The Maths Prof: Find Circumference of a Circle

  5. Math 5 Circumference of a Circle

  6. Calculating the Circumference of a Circle Given the Radius