Solve the Problem $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 81 } = \frac { z } { 2 }$

Multiple Choice

Solve the problem.
-Find the volume of the solid bounded by the paraboloid $\frac { x ^ { 2 } } { 49 } + \frac { y ^ { 2 } } { 81 } = \frac { z } { 2 }$ and the planes $z = 0$ and $z = 6$ . (The area of an ellipse with semiaxes $\mathrm { a }$ and $\mathrm { b }$ is $\pi \mathrm { ab }$ .)

A) $567 \pi$ units $^ { 3 }$
B) 567 units $^ { 3 }$
C) $1134 \pi$ units $^ { 3 }$
D) $567 \pi ^ { 2 }$ units $^ { 3 }$