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Area of a Circle Formula

  • Last Updated : 20 Dec, 2021

Circle is a collection of points that are at a fixed distance from a particular point. Every line passing through the circle forms the line of reflection symmetry. In addition to this, it has rotational symmetry around the center for every angle. Some of the examples of circles are wheels, pizzas, circular ground, etc. The distance from the center to the circle is known as radius.

Area of a circle is defined as is the region occupied by the circle in a two-dimensional plane. We can calculate the area of the circle in three ways.

Area of Circle using Radius

Area = πr2

where, 

r is the radius and π is the constant value

Example 1: If the length of the radius of a circle is 3 units. Calculate its area.

Solution:

We know that radius r = 3 units

So by using the above formulae:

Substitute r = 3.

As we know that π value = 3.14

3.14 × 3 × 3 = 28.26

Therefore, The area of the circle is 28.26 squared units.

Example 2: A large rope is in a circular shape. Its radius is 5 units. What is the area?

Solution:

A large rope is in circular shape means it is similar to circle, so we can use circle formulae to calculate the area of the large rope.

We know that radius r = 5 units

So by using the above formulae:

substitute r = 5.

As we know that π value = 3.14

3.14 × 3 × 3 = 28.26

Therefore, The area of the circle is 78.50 squared units.

Area of Circle using Diameter

Diameter of a circle is double the length of the radius of the circle, i.e. 2r

Area = (π/4) × d2  

where, 

d is the diameter of the circle.

Example 1: If the length of the diameter of a circle is 8 units. Calculate its area.

Solution:

We know that diameter = 8 units

so by using the above formulae:

substitute d = 8.

As we know that π value = 3.14

(3.14 /4) × 8 × 8 = 28.26

Therefore, The area of the circle is 50.24 squared units.

Example 2: If the length of the rope which is in circle shape is 4 units. Calculate its area.

Solution:

We know that length of rope is in circle. so its diameter= 4 units (given)

so by using the above formulae:

substitute d = 4.

As we know that π value = 3.14

(3.14 /4) × 4 × 4 = 28.26

Therefore, the area of the rope is 12.56 squared units.

Area of a Circle using Circumference

Circumference is defined as the length of the complete arc of a circle.

Area  = C2/4π

where, 

C is the circumference

Example 1: If the circumference of the circle is 4 units. Calculate its area.

Solution:

We know that circumference of the circle = 4 units (given)

so by using the above formulae:

substitute C = 4.

As we know that π value = 3.14

 4 × 4/(4 × 3.14) = 28.26

Therefore, The area of the circle is 1.273 squared units.

Example 2: If the circumference of the circle is 8 units. Calculate its area.

Solution:

We know that circumference of the circle = 8 units (given)

so by using the above formulae:

substitute C = 8.

As we know that π value = 3.14

8 × 8/(4 × 3.14) = 28.26

Therefore, the area of the circle is 5.09 squared units.

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