Solve the Problem $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 36$

question 116

Multiple Choice

Solve the problem.
-Find the center of mass of the region of constant density bounded from above by the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 36$ and from below by the cone $z = \sqrt { x ^ { 2 } + y ^ { 2 } }$ .

• A) \(\bar { x } = 0 , \bar { y } = 0 , \bar { z } = \frac { 9 } { 4 } ( 2 + \sqrt { 2 } )\)
• B) \(\bar { x } = 0 , \bar { y } = 0 , \bar { z } = \frac { 21 } { 8 } ( 2 + \sqrt { 2 } )\)
• C) \(\bar { x } = 0 , \bar { y } = 0 , \bar { z } = \frac { 15 } { 8 } ( 2 + \sqrt { 2 } )\)
• D) \(\bar { x } = 0 , \bar { y } = 0 , \bar { z } = \frac { 9 } { 8 } ( 2 + \sqrt { 2 } )\)

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