A ball of radius has a round hole of radius drilled through its center. Find the volume of the resulting solid.
this amounts to finding the volume of rotation for the region bounded by the curves $\displaystyle y = \sqrt{144 - x^2}$ and $\displaystyle y = 7$ revolved about the x-axis
or analogously, the region bounded by $\displaystyle y = \sqrt{144 - x^2}$ and $\displaystyle x = 7$ revolved about the y-axis