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2. Originally Posted by mjoshua
Here's the word problem I'm working on--the solution is $\displaystyle \frac{972}{\pi}$ but I get $\displaystyle 972 \pi$.

A student rolls a piece of rectangular construction paper so that the edges meet (but do not overlap) to form a right circular cylinder with no top or bottom. The cylinder is 12inches high and the paper has dimensions 12in by 18in. What is the volume of the cylinder?
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!

3. Ahh sorry about that Ivy--that makes sense now. I just halved the length to get 9 as the radius but didn't realize it was the circumference which equaled the rectangular length.

4. 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.