Theory and Examplesa. Find the volume of the solid bounded

Chapter 12, Problem 48E

(choose chapter or problem)

Problem        48E

Theory and Examples

a. Find the volume of the solid bounded by the hyperboloid

and the planes z = 0 and z = h, h > 0.

b. Express your answer in part (a) in terms of h and the areas and Ah of the regions cut by the hyperboloid from the planes z = 0 and z = h.

c. Show that the volume in part (a) is also given by the formula

where Am is the area of the region cut by the hyperboloid from the plane z = h/2.