...
The volume of a cylinder is given by $\displaystyle \pi r^2 h$ where r is the radius of the cylinder and h is the height.
You are told that the height of the cylinder is 12 in so the 18 in edge of the paper must form the circumference of the cylinder. Circumference is given by $\displaystyle 2\pi r$ so you must have $\displaystyle 2\pi r= 18$. Solve that for r and use h= 12.
Now, how did you get $\displaystyle 972 \pi$? We can't tell what you did wrong if you don't tell us what you did!
Hi mjoshua,
The volume of a cylinder is $\displaystyle \pi r^2 h $ where h is the height of the cylinder and r is the radius. The circumference of your cylinder is 18 inches and the height is 12 inches. The circumference = $\displaystyle 2 \pi r$. Therefore $\displaystyle r = \frac{18}{2\pi} = \frac{9}{\pi}$
The volume = $\displaystyle \pi. \frac{9}{\pi^2}^2. 12$
= $\displaystyle \frac{\pi.81.12}{\pi^2}$
= $\displaystyle \frac{972}{\pi}$
I hope this is clear.