Chapter 8, Problem 18P

A cylinder with base radius rand height h is constructed inside a sphere such that it is in contact with the surface of a sphere, as shown in the figure. The radius of the sphere is R = 11 in.

(a) Create a polynomial expression for the volume V of the cylinder in terms of h.

(b) Make a plot of V versus h for $0\le h\le 11$ in.

(c) Using the roots command determine h if the volume of the cylinder is 2000 in.3.

(d) Determine the value of h that corresponds to the cylinder with the largest possible volume, and determine that volume.