A solid cylinder of radius … is assembled from hollow cylinders of…

These problems find the other three J’s.

A solid cylinder of radius $r$ is assembled from hollow cylinders of length $l$, radius $x$, and volume $(2\pi x)(l)(dx)$. The solid cylinder has
$$\text{mass }M={\int }_0^{r}2\pi xl\rho dx\text{ and }I={\int }_0^r{x}^{2}2\pi xl\rho dx.$$
With $\rho =7$ find $M$ and $I$ and $J=I/M{r}^2$.

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §8.5 Masses and Moments, #35