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

question 221

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.

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