Solve the Problem $\delta ( x , y , z ) = \frac { 1 } { 36 - x ^ { 2 } - y ^ { 2 } }$

question 85

Multiple Choice

Solve the problem.
-Find the center of mass of the region of density $\delta ( x , y , z ) = \frac { 1 } { 36 - x ^ { 2 } - y ^ { 2 } }$ bounded by the paraboloid $z = 36 - x ^ { 2 } - y ^ { 2 }$ and the $x y$ -plane.

• A) \(\bar { x } = 0 , \bar { y } = 0 , \bar { z } = 2\)
• B) \(\bar { x } = 0 , \bar { y } = 0 , \bar { z } = 6\)
• C) \(\bar { x } = 0 , \bar { y } = 0 , \bar { z } = 3\)
• D) \(\bar { x } = 0 , \bar { y } = 0 , \bar { z } = \frac { 1 } { 2 }\)

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