Problems on Circles

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There are a lot of things that are circle-shaped around us. Like for example, the sun, pizza, coins, etc. are in the shape of a circle (two dimensional). It is quite different as compared to other shapes and figures in geometry.

However, before we move on with the problems on circles, first let’s recapitulate some essential points and features related to this shape.

What is Meant by a Circle?

In Mathematics, circles can be defined as a round-shaped figure with no edges or corners. Plus, lines drawn from the centre of a circle to the boundary are equidistant. Sketching a circle with hands is quite challenging, and so a compass is usually used for the same.

What are the Terms Associated to a Circle?

Here, we have organised a table representing the essential expression related to a circle. Take a look!




The distance between the centre of a circle to any point on the boundary is the radius


The line joining two boundary points of a circle provided that it passes through the centre is known as diameter.


A chord is a line joining two points on the boundary of a circle. You must note that diameter is the largest chord.

Tangent and Arc

A line touching any boundary point of a circle is called a tangent. Besides, any part of a circle’s circumference is an arc.

Formulas Required in Solving Circle Area and Circumference Word Problems

  • Area of a Circle

The expression to find an area of a circle is:

Area = π x r2, here r = radius

  • Perimeter of a Circle

The expression to find the perimeter of a circle is:

Perimeter = 2 x π x r, here also r = radius

  • Diameter of a Circle

The expression to find the diameter of a circle is:

Diameter = 2 x r

  • Area of a Semicircle

The formula to determine the area of a semicircle is:

Area of a semi circle = (π x r2) / 2

  • Perimeter of a Semi-circle

The expression to calculate the perimeter of a semicircle is:

Perimeter of a semi circle = π x r + 2 x r = (π + 2)r

Note: You can use 3.14 or 22/7 (the value of pi) as per your convenience unless mentioned in the problem.

Problems on Circles with Solutions

Problems on Circles: Problem 1

A circle has a diameter 142.8 mm. Find its radius.

Solution: Diameter of a circle = 142.8 mm

Therefore, putting the value in the equation to find the radius, we get:

d = 2 x r

142.8 = 2 x r

r = 142.8 / 2

r = 71.4 mm

Problems on Circles: Problem 2

What will be the radius of a circle having an area 200.96 sq Ft?

Solution: Area of the circle = 200.96 sq. Ft

Putting the value in the required equation we get:

Area = pi x r2

200.96 = 22/7 x r2

r2 = (200.96 / 3.14)

r2 = 64

r = 8 ft

Problems on Circles: Problem 3

When the diameter of a circular figure is 9 cm, find the radius and perimeter.

Solution: Diameter = 9 cm

Therefore, radius = 9/2 = 4.5 cm

Area = pi x r x r

Area = 3.14 x 4.5 x 4.5 = 63.585 cm sq.

Perimeter = 2 x pi x r

Perimeter = 2 x 3.14 x 4.5

Perimeter = 28.26 cm

Problems on Circles: Problem 4

Evaluate the perimeter and area of a semi-circle having a radius of 7 cm. Please use 22/7 as the value of pi.

Solution: Substituting the values in both the equations we get,

Perimeter of a semi circle = (π + 2)r = 22/7 x 7 + 2 x 7 = 22 + 14 = 36 cm

Area of a semi circle = (π x r2) / 2 = (22/7 x 49) / 2 = 77 cm sq.

Circle Math Problems: Do It Yourself

1. What will be the circumference of a circle whose area is 616 cm sq.?

(a) 88 cm (b) 89 cm (c) 84 cm (d) 80 cm

2. Evaluate the area of the circle inside the square, having each side measuring 20 cm. Refer to the image given below.

[Image will be Uploaded Soon]

(a) 341.2 cm sq. (b) 324.2 cm sq. (c) 314.2 cm sq. (d) 342.2 cm sq.

3. Calculate the perimeter of a semicircle with radius 10 cm.

(a) 54.12 cm (b) 51.42 cm (c) 52.41 cm (d) 52.14 cm

Problems on Circles: Answer Key

Question number




Right option




By going through the solved examples and working out the given sums, students will be able to predict the types of problems they can expect during exams. Furthermore, if you want to get enlightened with more circle geometry problems and solutions, why don’t you download the Vedantu app?

Make sure to download the same and get access to lots of study materials and online tutorials.

FAQ (Frequently Asked Questions)

1. What are the Properties of a Circle?

Ans. There are several features or properties of a circle. Firstly, when circles have similar radii, they are congruent. Secondly, the diameter of a circle divides the same into two arcs, named as a semi-circle. Thirdly, when the radii of two circles differ, but their centre is the same, they are termed as concentric circles.

2. What is the Importance of Circles?

Ans. In ancient Greece, circles were thought of to be the representation of ‘natural balance’ and ‘divine’, due to their symmetry. However, in the later period, this shape played a significant role during the invention of wheels, or circular shaped machines. Besides, monuments and structures made in the past show the importance of circles as well.

3. What are the Degrees of Angles in a Circle?

Ans. In general, all circles are segregated into 360 similar degrees, and students will only work with angles between 0 and 360 degrees. However, in advanced stages, when you will get to study trigonometric functions, negative angles, as well as angles more than 360 degrees, will be considered.