Solve the Problem $2 x ^ { 2 } + y ^ { 2 } + 4 z ^ { 2 } = 12$

question 127

Multiple Choice

Solve the problem.
-A rectangular box is to be inscribed inside the ellipsoid $2 x ^ { 2 } + y ^ { 2 } + 4 z ^ { 2 } = 12$ . Find the largest possible volume for the box.

• A) \(16 \sqrt { 2 }\)
• B) \(15 \sqrt { 2 }\)
• C) \(12 \sqrt { 2 }\)
• D) \(18 \sqrt { 2 }\)

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