# Why is the area of a circle given by the formula #pir^2# ?

##### 1 Answer

Aug 31, 2016

See explanation...

#### Explanation:

The circumference of a circle is

If we take a circle of radius

If we use a larger number of thin segments, then this is more like a rectangle with height

Here's an animation for just

So the area of the circle is proportional to the square of the radius.