freeCodeCamp/guide/english/mathematics/area-of-a-circle/index.md

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Area of a Circle

Area of a Circle

The area of a circle is all the space inside a circle's circumference.

If 'r' is the radius of circle, its area is calculated with formula πr² where π is mathematical constant.

π ≈ 22/7 ≈ 3.141592....

A = π *r², r is the radius of circle

A = π * {d²/4}, d is the diameter of circle, d=2* r

Area of a circle is defined as the space enclosed by the circumference of the circle.

Terminology

Circumference (C) - The enclosing boundary of the circle is called circumference of the circle.

Radius (r) - The length of a line from any point on the boundary/cirumference of the circle to the centre of the circle is known as the radius of the circle.

Diameter (d) - The length of the line that passes across the circle through the centre of the circle, is called the diameter.

Pi (π) - A mathematical constant which is approximated as 3.14

Formula

Area = π × r²

Given radius of the circle

Area of circle = π * radius²

Given diameter of the circle

We know that diameter = 2 * radius, so you can derive the area of the circle as below,

Area of circle = π * (diameter/2)²

Given circumference of the circle

We know that the circumference of the circle (C),
C = 2 * π * (radius).

From this, you can derive the area of the circle as below,

Area of circle = C² / 4 * π

Examples

1. Given radius = 3cm, find area of the circle

   Area = 3.14 * 9 = 28.26 cm²

2. Given diameter = 8cm, find area of the circle

   Radius = (Diameter/2) = 4cm

   Area = 3.14 * 16 = 50.24 cm²

3. Given circumference of a circle = 25cm, find the area of the circle

   Area = 625 / (4 * 3.14) = 49.76 cm²

A "Real World" Example:-

Example: Max is building a house. The first step is to drill holes and fill them with concrete. The holes are 0.4 m wide and 1 m deep, how much concrete should Max order for each hole?

The holes are circular (in cross section) because they are drilled out using an auger. The diameter is 0.4m, so the Area is: A = (π/4) × D2 A = (3.14159.../4) × 0.42 A = 0.7854... × 0.16 A = 0.126 m2 (to 3 decimals) And the holes are 1 m deep, so: Volume = 0.126 m2 × 1 m = 0.126 m3 So Max should order 0.126 cubic meters of concrete to fill each hole.

Note: Max could have estimated the area by:

1. Calculating a square hole: 0.4 × 0.4 = 0.16 m2
2. Taking 80% of that (estimates a circle): 80% × 0.16 m2 = 0.128 m2
3. And the volume of a 1 m deep hole is: 0.128 m3

More Information

More information with illustrations can be found WikiHow