Question

How do you use the polar coordinates to find the volume of a sphere of radius 10?

Answer 1

`(4000pi)/3`

Explanation:

Volume of a sphere in spherical coordinates is `dV=r^2 sin phi dr theta d phi`Thus V=`int_(phi=0) ^pi int_(theta=0)^(2pi) int_(r=0)^10 r^2 sinphi dr d theta d phi`

=`1000/3int_(phi=0) ^pi int_(theta=0)^(2pi) sinphi d theta d phi`

`(2000pi)/3int_(phi=0) ^pi sinphid phi`

=`(2000pi)/3 [-cosphi]_0^pi`=`(4000pi)/3`