Solve the Problem $$\iiint _ { R } \int \sqrt { 1 - \left( \frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } + \frac { z ^ { 2 } } { 9 } \right) } d x d y d z$$

Multiple Choice

Solve the problem.
-Evaluate
$$\iiint _ { R } \int \sqrt { 1 - \left( \frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } + \frac { z ^ { 2 } } { 9 } \right) } d x d y d z$$
where $R$ is the interior of the ellipsoid $\frac { x ^ { 2 } } { 25 } + \frac { y ^ { 2 } } { 16 } + \frac { z ^ { 2 } } { 9 } = 1$ . Hint: Let $x = 5 u , y = 4 v , z = 3 w$ , and then convert to spherical coordinates.

A) $15 \pi$
B) $20 \pi$
C) $20 \pi ^ { 2 }$
D) $15 \pi ^ { 2 }$