Find the volume of a sphere using integrals and the disk method.
Problem
Find the volume of a sphere generated by revolving the semicircle y = √
(R 2 - x 2) around the x axis.
Solution
The graph of y = √(R 2 - x 2) from x = - R to x = R is shown below. Let f(x) = √(R 2 - x 2), the volume is given by formula 1 in Volume of a Solid of Revolution
Figure 1. volume of a sphere generated by the rotation of a semi circle around x axis
This is the very well known formula for the volume of the sphere. If you revolve a semi circle of radius R around the x axis, it will generate a sphere of radius R.