Set Up and Evaluate the Integral That Gives the Volume $y = x ^ { 8 }$

Multiple Choice

Set up and evaluate the integral that gives the volume of the solid formed by revolving the region bounded by $y = x ^ { 8 }$ and $y = 256$ in the first quadrant about the $y$ -axis.

A) $V = \pi \int _ { 0 } ^ { 8 } y ^ { \frac { 1 } { 8 } } d y = \frac { 4,096 } { 5 } \pi$
B) $V = \pi \int _ { 0 } ^ { 8 } y ^ { \frac { 1 } { 4 } } d y = \frac { 2,048 } { 5 } \pi$
C) $V = \pi \int _ { 0 } ^ { 256 } y ^ { \frac { 1 } { 4 } } d y = \frac { 2,048 } { 5 } \pi$
D) $V = \pi \int _ { 0 } ^ { 256 } y ^ { \frac { 1 } { 8 } } d y = \frac { 2,048 } { 5 } \pi$
E) $V = \pi \int _ { 0 } ^ { 256 } y ^ { \frac { 1 } { 4 } } d y = \frac { 4,096 } { 5 } \pi$