A cone with base radius r and vertex in contact with the surface of a sphere is constructed inside a sphere, as shown in the figure. The radius of the sphere is R = 9 in.
(a) Create a polynomial expression for the volume V of the cone in terms of h.
(b) Make a plot of V versus h for 9 (c) Using the roots command determine h if the volume of the cone is 500 in.3.
(d) Determine the value of h that corresponds to the cone with the largest possible volume, and determine that volume.

R.