Chapter 6.2, Problem 55ES

The accompanying figure shows a spherical cap of radius $\rho$ and height $h$ cut from a sphere of radius $r$ . Show that the volume $V$ of the spherical cap can be expressed as

(a) $V=\frac{1}{3}\pi h^2\left(3r-h\right)$

(b) $V=\frac{1}{6}\pi h\left(3{\rho }^2+h^2\right)$ .