Find the moment of inertia of a uniform solid cone about its central axis, which is the axis of symmetry perpendicular to the base. The cone has a base radius $R_{b}$, height $h$, and mass $m$ . Assume the cone is made of aluminum.
Hint: Consider the cone as composed of a stack of infinitesimally thin disks, each having a different radius that decreases linearly from the base to the tip as you move along the height.

• A. $\begin{array}{l}\frac{1}{3}mR_b^2\end{array}$
• B. $\begin{array}{l}\frac{1}{2}mR_b^2\end{array}$
• C. $\begin{array}{l}\frac{3}{10}mR_b^2\end{array}$
• D. $\begin{array}{l}\frac{13}{10}mR_b^2\end{array}$

Answer: (C)