Solve the Problem $$\iiint \left( 1 - \frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 64 } - \frac { z ^ { 2 } } { 64 } \right) d V ?$$

Multiple Choice

Solve the problem.
-What domain D in space minimizes the value of the integral
$$\iiint \left( 1 - \frac { x ^ { 2 } } { 64 } - \frac { y ^ { 2 } } { 64 } - \frac { z ^ { 2 } } { 64 } \right) d V ?$$

A) $\mathrm { D } =$ the boundary and interior of the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 64$ .
B) $D =$ the boundary of the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 64$ .
C) $\mathrm { D } = 23$
D) No such maximum domain exists.