The Disk $( x - 4 ) ^ { 2 } + y ^ { 2 } \leq 1$

Multiple Choice

The disk $( x - 4 ) ^ { 2 } + y ^ { 2 } \leq 1$ is revolved about the $y$ -axis to generate a torus. Find its volume. (Hint: $\int _ { - 1 } ^ { 1 } \sqrt { 1 - y ^ { 2 } } d y = \frac { 1 } { 2 } \pi$ , since it is the area of a semicircle of radius 1 .)

A) $8 \pi ^ { 2 }$
B) $2 \pi ^ { 2 }$
C) $4 \pi ^ { 2 }$
D) $4 \pi$