In **Mensuration** the circumference and area of a circle are defined as the length of the boundary of the circle and region occupied by the circle in 2-D Geometry. Let us discuss in detail the area and circumference of the circle using the formulas and solved example problems. We provide a detailed explanation of how to calculate the circumference and area of the circle.

## What is Circumference and Area of Circle?

**Circumference of Circle:**

The circumference of the circle is the measure of the boundary of the circle. The circumference of the circle is also known as the perimeter of the circle. The perimeter or circumference of the circle is measured in units.

C = Πd or 2Πr

**Area of Circle:
**

The area of the circle is the region covered by the circle or sphere in two-dimensional mensuration. The units to measure the area of the circle is square units.

A = Πr²

Where,

A is the area of the circle

r is the radius of the circle

### What is the radius of the circle?

The radius of the circle is the distance from the center to the outline of the circle. Radius plays an important role in calculating the area and perimeter of the circle.

### Properties of Circle

The properties of the circle are given below,

- The diameter of the circle is the longest chord of the circle.
- The circle is said to be congruent if it has the same radii.
- A circle can confine rectangle, square, trapezium, etc.
- If the tangents are drawn at the end of the diameter they are parallel to each other.

### Area and Circumference of Circle Formula

**Circumference:**

The circumference of the circle is the measure of the boundary of the circle. The formula for the circumference of the circle is given below,

C = Πd

Where,

C is the circumference of the circle

Π is the mathematical constant

The approximate value of pi is 3.14 or 22/7

d is the diameter of the circle

C = 2Πr

Where,

C is the circumference of the circle

Π is the mathematical constant

The approximate value of pi is 3.14 or 22/7

r is the radius of the circle

**Area: **

The formula for the area of the circle is as follows,

A = Πr²

A is an area of the circle

Π is the mathematical constant

The approximate value of pi is 3.14 or 22/7

r is the radius of the circle

**Area of Semi-Circle:**

The area of the semicircle is the region covered by the 2D figure. The formula for the area of the semi-circle is as follows,

A = Πr²/2

**Perimeter of the Semi-circle:**

The formula for the perimeter of the semi-circle is given below,

P = 2Πr/2 = Πr

### Solved Examples on Circumference and Area of a Circle?

Get the step by step explanation on the formula of Area and Circumference of Circle here.

**1. What is the circumference of the circle with a radius of 7cm?**

Solution:

Given,

r = 7cm

We know that,

Circumference of the circle = 2Πr

C = 2 × 22/7 × 7 cm

C = 44 cm

Thus the circumference of the circle is 44 cm.

**2. What is the circumference of the circle with a diameter of 21 cm?**

Solution:

Given,

d = 21 cm

We know that,

Circumference of the circle = 2Πr

C = Πd

C = 22/7 × 21cm

C = 22 × 3cm

C = 66 cm

Therefore the circumference of the circle is 66 cm.

**3. Find the area of the circle with a radius of 14m?**

Solution:

Given,

r = 14m

We know that,

Area of Circle = Πr²

A = 22/7 × 14 × 14 sq.m

A = 22 × 2 × 14 m²

Thus the area of the circle is 616m²

**4. Find the area of the circle if its circumference is 124m?**

Solution:

Given,

Circumference of the circle = 124m

We know that,

Circumference of the circle = 2Πr

124m = 2Πr

Πr = 124/2

Πr = 62

r = 62 × 7/22

r = 19.72 m

Now find the area of the circle using the radius.

Area of Circle = Πr²

A = 3.14 × (19.72)²

A = 1221 sq. m

Therefore the area of the circle is 1221 sq. meters.

**5. Find the area and circumference of the circle of radius 14m?**

Solution:

Given,

radius = 14m

We know that,

Circumference of the circle = 2Πr

C = 2 × 22/7 × 14m

C = 2 × 22 × 2m

C = 88m

Now find the area of the circle using the radius.

Area of Circle = Πr²

A = Π(14)²

A = 22/7 × 14 × 14 sq.m

A = 22 × 2 × 14

A = 44 × 14 sq.m

A = 616 sq.m

Thus the area of the circle is 616 sq.m

### FAQs on Circumference and Area of Circle

**1. How to calculate the area of a circle?**

The area of the circle can be calculated by the product of pi and radius squared.

**2. What is the diameter of the circle?**

The diameter of the circle is 2r.

**3. How to calculate the circumference of the circle?**

The circumference of the circle can be calculated by multiplying the diameter with pi.