Chapter 6.2, Problem 38ES

Consider the solid generated by revolving the shaded region in Exercise $4$ about the line $x=2.5$ .

(a) Make a conjecture as to which is larger: the volume of this solid or the volume of the solid in Exercise $4$ . Explain the basis of your conjecture.

(b) Check your conjecture by calculating this volume and comparing it to the volume obtained in Exercise $4$ .