Solve the problem.
-Find the moment of inertia about the z-axis of a thick-walled right circular cylinder bounded on the inside by the cylinder r = 1, on the outside by the cylinder r = 2, and on the top and bottom by the planes
Z = 7 and z = 11.
A) $30 \pi$
B) $15 \pi$
C) $32 \pi$
D) $60 \pi$

Question

Solve the problem.
-Find the moment of inertia about the z-axis of a thick-walled right circular cylinder bounded on the inside by the cylinder r = 1, on the outside by the cylinder r = 2, and on the top and bottom by the planes
Z = 7 and z = 11. 
A) $30 \pi$
B) $15 \pi$
C) $32 \pi$
D) $60 \pi$

Quizplus · Accepted Answer

The moment of inertia about the z-axis for a thick-walled cylinder can be calculated using the formula $I_z = \frac{1}{2} M (R^2 + r^2)$, where $M$ is the mass of the cylinder, $R$ is the outer radius, and $r$ is the inner radius. The height $h$ of the cylinder is $11 - 7 = 4$, and the volume $V$ of the material is $\pi h (R^2 - r^2) = \pi \cdot 4 \cdot (2^2 - 1^2) = 12\pi$. Assuming a uniform density $\rho$, the mass $M = \rho V = 12\pi\rho$. Substituting $M$, $R$, and $r$ into the formula gives $I_z = \frac{1}{2} \cdot 12\pi\rho \cdot (2^2 + 1^2) = 6\pi\rho \cdot 5 = 30\pi\rho$. Since the problem does not specify the density $\rho$, and we are interested in the formulaic result, the answer is $30\pi$, assuming a uniform density that would cancel out in the comparison of choices.

Solve the Problem 30π30 \pi30π B) 15π15 \pi15π C) 32π32 \pi32π D) 60π60 \pi60π

Solve the Problem $30 \pi$ B) $15 \pi$ C) $32 \pi$ D) $60 \pi$