Let V Be the Volume of the Solid That Lies $y = \frac { x ^ { 2 } } { 8 }$

Multiple Choice

Let V be the volume of the solid that lies between planes perpendicular to the x-axis from x = 0 to x = 4. The cross-sections of this solid perpendicular to the x-axis run from $y = \frac { x ^ { 2 } } { 8 }$ to $y = \sqrt { x }$ and they are equilateral triangles with bases in the xy-plane. Then V is

A) $\frac { 72 \sqrt { 3 } } { 35 }$
B) $\frac { 36 \sqrt { 3 } } { 33 }$
C) $\frac { 18 \sqrt { 3 } } { 33 }$
D) $\frac { 18 \sqrt { 3 } } { 35 }$
E) $\frac { 12 \sqrt { 3 } } { 35 }$