Volume of bounded area
First let's consider this within the XY-plane
is the equation for the top half (since the root symbol restricts us to non-negative vales) of a circle with center the origin and radius
bounding this by
implies we are dealing (within the XY-plane) with a quarter circle (whose radius is
If we rotate this about the X-axis we will obtain half of a sphere.
The volume of a sphere is
Here the radius,