Circumference and Area of a Circle

Introduction

• Circle is very important shape in Geometry. Since it is used in various fields its study is important.
• Understanding the concepts of Area and Circumference of a Circle is crucial as it is applied in real life like Construction and even in our daily life measurements. Some of them are –

Circumference of A Circle

• The Perimeter of a Circle is Circumference. Basically it is the length of circle’s boundary. It is one-dimensional.
• Circumference is used to find the length of a track or wheel’s perimeter like problems in real life.
• We can find Circumference of a Circle using its radius with the help of following formula –

Solved Example

Find the Circumference of the Circle with radius 10 cm.

SOLUTION

Formula:

$$Circumference = 2\pi r$$

$$Circumference = (2 \times 3.14 \times 10)\text{ cm}$$

$$Circumference = 62.8\text{ cm}$$

Final Answer: $62.8 \text{ cm}$

Area of A Circle

• The space enclosed by circumference of Circle is called its Area. It is two-dimensional.
• Used to measure the circular object’s area present in real life.
• The formula of Area of circle is:

Solved Example

Find the Area of the Circle with radius 10 cm.

SOLUTION

Formula:

$$Area = \pi r^{2}$$

$$Area = (3.14 \times 10 \times 10)\text{ cm}^{2}$$

$$Area = 314\text{ cm}^{2}$$

Final Answer: $314 \text{ cm}^2$

Solved Examples

Solved Example

Find out the Circumference and area of the following circles using there diameters.

SOLUTION

First we find the radius of the circle:

(a) Diameter = 4 cm

Radius: $Radius = \frac{4}{2} = 2\text{cm}$

Circumference:

$$Circumference = 2\pi r$$

$$Circumference = (2 \times 3.14 \times 2)\text{ cm}$$

$$Circumference = 12.56\text{ cm}$$

Area:

$$Area = \pi r^{2}$$

$$Area = (3.14 \times 2 \times 2)\text{ cm}^{2}$$

$$Area = 12.56\text{ cm}^{2}$$

(b) Diameter = 6 cm

Radius: $Radius = \frac{6}{2} = 3\text{cm}$

Circumference:

$$Circumference = 2\pi r$$

$$Circumference = (2 \times 3.14 \times 3)\text{ cm}$$

$$Circumference = 18.84\text{ cm}$$

Area:

$$Area = \pi r^{2}$$

$$Area = (3.14 \times 3 \times 3)\text{ cm}^{2}$$

$$Area = 28.26\text{ cm}^{2}$$

Final Answer: (a) $12.56 \text{ cm}^2$ and (b) $28.26 \text{ cm}^2$

Solved Example

Find out the Circumference and area of the circle in terms of $\pi$?

SOLUTION

The diameter of the circle is given using it we can find the circumference:

Circumference:

$$Circumference = \pi \times \text{diameter}$$

$$Circumference = (\pi \times 12)\text{ cm}$$

$$Circumference = 12\pi\text{ cm}$$

Area:

To find the area, first find the radius:

Radius: $Radius = \frac{12}{2} = 6\text{cm}$

$$Area = \pi r^{2}$$

$$Area = \pi (6)^{2}$$

$$Area = 36\pi\text{ cm}^{2}$$

Final Answer: $36\pi \text{ cm}^2$

Solved Example

Fill in the blanks

SOLUTION

(1) The Diameter of the Circle is 20cm, So:

(2) The Circumference is given with which we can find the diameter of Circle:

Circumference = $56.52 \text{ cm}$

We can write –

From diameter:

(3) The Radius of the Circle is 5cm, So:

Completed Table:

Sr. No.	RADIUS	DIAMETER	AREA	CIRCUMFERENCE
1	10 cm	20 cm	$314\text{ cm}^{2}$	$62.8\text{ cm}$
2	9 cm	18 cm	$254.34\text{ cm}^{2}$	$56.52\text{ cm}$
3	5 cm	10 cm	$78.50\text{ cm}^{2}$	$31.4\text{ cm}$

Final Answer: Missing values successfully calculated above.