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

2 Answers
1s2s2p
Mar 16, 2018

#V=4/3pir^3#

George C.
Mar 16, 2018

#v = 4/3 pir^3#

Explanation:

The surface area of a sphere of radius #r# is #4pi r^2#

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 #1/3 xx "base" xx "height"#

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#

Related questions
See all questions in Volume of Solids
Impact of this question
8705 views around the world
You can reuse this answer
Creative Commons License