Let V Be the Volume of the Solid That Lies $y = - 4 \sqrt { 1 - x ^ { 2 } }$

Multiple Choice

Let V be the volume of the solid that lies between planes perpendicular to the x-axis from x = -1 to x = 1. The cross-sections of this solid perpendicular to the x-axis run from $y = - 4 \sqrt { 1 - x ^ { 2 } }$ to $y = 4 \sqrt { 1 - x ^ { 2 } }$ and they are equilateral triangles with bases in the xy-plane. Then V is

A) $\frac { 256 } { \sqrt { 3 } }$
B) $\frac { 128 } { \sqrt { 3 } }$
C) $\frac { 64 } { \sqrt { 3 } }$
D) $\frac { 32 } { \sqrt { 3 } }$
E) $\frac { 16 } { \sqrt { 3 } }$