Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the indicated line. $y = 4 - x ^ { 2 } , y = 0 ;$ the line $y = 6$
A) $\frac { 704 } { 15 } \pi$
B) $\frac { 1408 } { 15 } \pi$
C) $\frac { 2816 } { 15 } \pi$
D) $\frac { 1408 } { 5 } \pi$

Question

Quizplus · Accepted Answer

The volume of the solid is found using the method of cylindrical shells or washers. The region is revolved around the line $y = 6$, and the volume is calculated using the washer method, integrating the difference of squares of the outer and inner radii from the intersection points of the curves.

Find the Volume of the Solid Generated by Revolving the Region