Step 1:

$\pi \large\frac{r^2}{h^2}\bigg[\frac{x^3}{3}\bigg]_0^h$

$\quad=\large\frac{\pi}{3}\frac{r^2}{h^2}.$$h^3$

$\quad=\large\frac{1}{3} $$\pi r^2 h \;units$

Step 2:

The volume of the solid generated by the shaded region about the x axis is $v=\int \limits_0^1 \pi y^2 dx$

Step 3:

$\qquad=\pi \int \limits_0^1 \large\frac{1}{x^2}\;$$dx$

$\qquad=\pi \bigg[\large\frac{-1}{x}\bigg]_0^1$