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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The Answer of 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) $I _ { Z } = 8 \pi$

Solve the Problem zzz -Axis Shell: "Nose" of the Paraboloid x2+y2=2zx ^ { 2 } + y ^ { 2 } = 2 zx2+y2=2z

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