Solve the Problem $z$ -Axis Shell: "Nose" of the Paraboloid $x ^ { 2 } + y ^ { 2 } = 2 z$

question 64

Multiple Choice

Solve the problem.
-The shape and density of a thin shell are indicated below. Find the moment of inertia about the $z$ -axis. Shell: "nose" of the paraboloid $x ^ { 2 } + y ^ { 2 } = 2 z$ cut by the plane $z = 2$
Density: $\delta = \frac { 1 } { \sqrt { x ^ { 2 } + y ^ { 2 } + 1 } }$

• A) \(I _ { Z } = \frac { 64 } { 3 } \pi\)
• B) \(\mathrm { I } _ { \mathrm { Z } } = 128 \pi\)
• C) \(\mathrm { I } _ { Z } = \frac { 16 } { 3 } \pi\)
• D) \(I _ { Z } = 8 \pi\)

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