Let V Be the Volume of the Solid That Lies $y = \frac { x ^ { 2 } } { 9 }$

Multiple Choice

Let V be the volume of the solid that lies between planes perpendicular to the x-axis from x = 0 to x = 3. The cross-sections of this solid perpendicular to the x-axis run from $y = \frac { x ^ { 2 } } { 9 }$ to $y = \sqrt { \frac { x } { 3 } }$ and they are equilateral triangles with bases in the xy-plane. Then V is

A) $\frac { 27 \sqrt { 3 } } { 280 }$
B) $\frac { 27 \sqrt { 3 } } { 140 }$
C) $\frac { 27 \sqrt { 3 } } { 70 }$
D) $\frac { 27 \sqrt { 3 } } { 35 }$
E) $\frac { 27 \sqrt { 3 } } { 350 }$