How to find the volume of a sphere using integration?

1 Answer
Sep 18, 2014

Since a sphere with radius r can be obtained by rotating the region bounded by the semicircle y=r2x2 and the x-axis about the x-axis, the volume V of the solid can be found by Disk Method.

V=πrr(r2x2)2dx

by the symmetry about the y-axis,

=2πr0(r2x2)dx

=2π[r2xx33]r0

=2π(r3r33)

=43πr3