Solve the Problem $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 81 } = \frac { z ^ { 2 } } { 16 }$

Multiple Choice

Solve the problem.
-Find the volume of the solid bounded by the elliptical cone $\frac { x ^ { 2 } } { 64 } + \frac { y ^ { 2 } } { 81 } = \frac { z ^ { 2 } } { 16 }$ and the planes $z = 0$ and $z = 4$ . (The area of an ellipse with semiaxes $a$ and $b$ is $\pi a b$ .)

A) $24 \pi$ units $^ { 3 }$
B) $288 \pi$ units $^ { 3 }$
C) $96 \pi$ units $^ { 3 }$
D) 96 units $^ { 3 }$