Solve the Problem $x ^ { 2 } + y ^ { 2 } - z ^ { 2 } = 0$

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: portion of the cone $x ^ { 2 } + y ^ { 2 } - z ^ { 2 } = 0$ between $z = 1$ and $z = 2$
Density: $\delta = 1$

A) $\mathrm { I } _ { \mathrm { Z } } = 15$
B) $\mathrm { I } _ { \mathrm { Z } } = \frac { 15 } { 2 } \sqrt { 2 } \pi$
C) $\mathrm { I } _ { \mathrm { Z } } = 15 \pi$
D) $\mathrm { I } _ { \mathrm { Z } } = \frac { 15 } { 2 } \sqrt { 2 }$