Chapter 5.4, Problem 7P

As needed, use a computer to plot graphs of figures and to check values of integrals

1. Using spherical coordinates, find the volume cut from the ball $r\le a$ by the cone $\theta =a<\pi /2$.
2. Show that the z coordinate of the centroid of the volume in (a) is given by the formula $\bar{z}=3a\left(1+\cos \alpha \right)/8$.