91 lines
3.0 KiB
Markdown
91 lines
3.0 KiB
Markdown
---
|
||
title: 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 πr<sup>2</sup> where π is mathematical constant.
|
||
|
||
π ≈ 22/7 ≈ 3.141592....
|
||
|
||
A = π *r<sup>2</sup>, r is the radius of circle
|
||
|
||
A = π * {d<sup>2</sup>/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 (<span class="texhtml">π</span>) - A mathematical constant which is approximated as 3.14
|
||
|
||
#### Formula
|
||
Area = π × r<sup>2</sup>
|
||
|
||
###### Given radius of the circle
|
||
|
||
Area of circle = <span class="texhtml"><span class="texhtml">π</span> * <i>radius</i><sup>2</sup></span>
|
||
|
||
###### 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 = <span class="texhtml"><span class="texhtml">π</span> * <i>(diameter/2)</i><sup>2</sup></span>
|
||
|
||
###### Given circumference of the circle
|
||
|
||
We know that the circumference of the circle (C),
|
||
<br>`C = 2 * π * (radius)`.
|
||
<br><br>From this, you can derive the area of the circle as below,
|
||
|
||
Area of circle = <i>C</i><sup>2</sup></span> / 4 * <span class="texhtml"><span class="texhtml">π</span>
|
||
|
||
#### Examples
|
||
|
||
1. Given radius = 3cm, find area of the circle
|
||
|
||
Area = 3.14 * 9 = 28.26 <span>cm<sup>2</sup></span>
|
||
|
||
2. Given diameter = 8cm, find area of the circle
|
||
|
||
Radius = (Diameter/2) = 4cm
|
||
|
||
Area = 3.14 * 16 = 50.24 <span>cm<sup>2</sup></span>
|
||
|
||
3. Given circumference of a circle = 25cm, find the area of the circle
|
||
|
||
Area = 625 / (4 * 3.14) = 49.76 <span>cm<sup>2</sup></span>
|
||
|
||
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](https://www.wikihow.com/Calculate-the-Area-of-a-Circle)
|
||
|