Let V be the volume of the solid generated by revolving the region enclosed by $y = 2 x ^ { 2 },$ the x-axis, $x = 1 ;$ about the x-axis. Then V is

A) $\frac { 4 \pi } { 3 }$
B) $\frac { 4 \pi } { 5 }$
C) $\frac { 8 \pi } { 3 }$
D) $\frac { 8 \pi } { 5 }$
E) $\frac { \pi } { 5 }$

Question

Let V be the volume of the solid generated by revolving the region enclosed by $y = 2 x ^ { 2 },$ the x-axis, $x = 1 ;$ about the x-axis. Then V is

A) $\frac { 4 \pi } { 3 }$
B) $\frac { 4 \pi } { 5 }$
C) $\frac { 8 \pi } { 3 }$
D) $\frac { 8 \pi } { 5 }$
E) $\frac { \pi } { 5 }$

Quizplus · Accepted Answer

The volume of the solid of revolution is calculated using the disk method: $ V = \pi \int_{0}^{1} (2x^2)^2 \, dx = \pi \int_{0}^{1} 4x^4 \, dx = \pi \left[ \frac{4}{5}x^5 \right]_{0}^{1} = \frac{4\pi}{5} $.

Let V Be the Volume of the Solid Generated by Revolving