Surface Area of Circle Formula

A circle is made up of points that are all at the same distance from the circle's centre. A closed geometric form is a circle. In everyday life, we see circles in the form of a wheel, pizzas, a round ground, and so on. 

Parts of a Circle

Key Terms:

• Radius: The radius of a circle is the distance between its centre and any point on the edge. It is generally denoted as r. A circle has an endless number of radii.
• Diameter: It is a line that runs through the centre and has its ends on the circle. It is denoted as D and is twice the value of the radius of the circle.
• Circumference: The extent of the circle's border equals its circumference. This signifies that a circle's perimeter equals its circumference. The circumference of the circle will be equal to the length of the thread that neatly wraps around its perimeter. It is given as 2πr.

Area of Circle

The area of a circle relates to the quantity of space encompassed by a circle's edge. The area filled by the circle is the territory within the circle's perimeter. It's also known as the total quantity of square units included within the circle.

Check: Diameter of a circle

Area of Circle Formulas

The area of a circle is given by the following formula:

Using the radius: A = πr²

where,

• A is the area of the circle.
• r is the radius of the circle.

Using the circumference: A = C²/4π

where,

• A is the area of the circle.
• C is the circumference of the circle.

Note: The numerical calculations in the following examples use π ≈ 3.14. If you use a more precise value of π (such as 3.1416 or the π key on a scientific calculator), the final answers may differ slightly due to rounding.

Solved Examples

Question 1. Find the area of a circle given its radius is 8 m.

Solution:

Given: r = 8 m

Since area of a circle = πr²

A = π(8)²

= 64π

= 200.96 m²

Question 2. Find the area of a circle given its circumference is 12 cm.

Solution:

Given: C = 12 cm

Since, A = C²/4π

= 12²/4π

= 11.46 cm²

Question 3. Find the area of a circle given its diameter is 12 cm.

Solution:

Given: D = 12 cm

or, Radius = r = 12/2 = 6 cm

Since A = πr²

= π(6)2

= 113.04 cm²

Question 4. Find the area of a circle given its radius is 9 cm.

Solution:

Given: r = 9 cm

Since area of a circle = πr²

A = π(9)²

= 81π

= 254.34 cm²

Question 5. Find the area of a circle given its diameter is 10 cm.

Solution:

Given: D = 10 cm

or, Radius = r = 10/2 = 5 cm

Since A = πr²

= π(5)²

= 78.5 cm²