Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given lines. $y = x ^ { 2 } , y = 8 x - x ^ { 2 }$
(i) $x$-axis;
(ii) the line $y = 18$
A) $\frac { 1,024 } { 3 } \pi ; \frac { 1,280 } { 3 } \pi$
B) $\frac { 16 } { 3 } \pi ; \frac { 1,280 } { 3 } \pi$
C) $\frac { 64 } { 3 } \pi ; \frac { 128 } { 3 } \pi$
D) $\frac { 64 } { 3 } \pi ; \frac { 1,280 } { 3 } \pi$
E) $\frac { 16 } { 3 } \pi ; \frac { 128 } { 3 } \pi$

Question

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given lines. $y = x ^ { 2 } , y = 8 x - x ^ { 2 }$
(i) $x$-axis; 
(ii) the line $y = 18$
A) $\frac { 1,024 } { 3 } \pi ; \frac { 1,280 } { 3 } \pi$
B) $\frac { 16 } { 3 } \pi ; \frac { 1,280 } { 3 } \pi$
C) $\frac { 64 } { 3 } \pi ; \frac { 128 } { 3 } \pi$
D) $\frac { 64 } { 3 } \pi ; \frac { 1,280 } { 3 } \pi$
E) $\frac { 16 } { 3 } \pi ; \frac { 128 } { 3 } \pi$

Quizplus · Accepted Answer

The correct answer is A because the volume of the solid generated by revolving the region bounded by the graphs of the equations about the x-axis is $\frac { 1,024 } { 3 } \pi$ and the volume of the solid generated by revolving the region bounded by the graphs of the equations about the line $y = 18$ is $\frac { 1,280 } { 3 } \pi$.

Find the Volume of the Solid Generated by Revolving the Region