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

question 145

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 \(^ { 3 }\)

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