# What is the volume #v# of a sphere of radius #r#?

##### 2 Answers

Mar 16, 2018

Mar 16, 2018

#### Explanation:

The surface area of a sphere of radius

Imagine dissecting a sphere into a large number of slender pyramids, with apices at the centre and (slightly rounded) bases tesselating the surface. As you use more pyramids, the bases get flatter.

The volume of each pyramid is

So the total volume of all the pyramids is:

#v = sum 1/3 xx "base" xx "height" = r/3 sum "base" = r/3 * 4pir^2 = 4/3 pir^3#