For detailed information about sphere, see the Solid Geometry entry, The Sphere.
The formula for the volume of the sphere is given by
Where, r = radius of the sphere
Derivation for Volume of the Sphere
The differential element shown in the figure is cylindrical with radius x and altitude dy. The volume of cylindrical element is...
The sum of the cylindrical elements from 0 to r is a hemisphere, twice the hemisphere will give the volume of the sphere. Thus,
From the equation of the circle x2 + y2 = r2; x2 = r2 - y2.