Chapter 5.3, Problem 178E

A spherical cap is the region of a sphere that lies above or below a given plane.

a. Show that the volume of the spherical cap in the figure below is $\frac{1}{6}\pi h\left(3a^2+h^2\right)$

b. A spherical segment is the solid defined by intersecting a sphere with two parallel planes. If the distance between the planes is Ii. show that the volume of the spherical segment in the figure below is $\frac{1}{6}\pi h\left(3a^2+3b^2+h^2\right)$