# Math Help - Thickness of Cylindrical Pipe

1. ## Thickness of Cylindrical Pipe

The volume of a metallic cylindrical pipe is 748 cu.cm. Its length is 14 cm & its external radius is 9 cm. How do I find its thickness?

This is what I tried:

pi x r x r x h = 748
pi x r x r x 14 = 748
r x r = 17
r = 4.17 (this is the internal radius)

thickness = 9 - 4.17 = 5.83 cm

But the answer is wrong. Can someone help me out with this?

Thanks,

Ron

2. Let $r_{out}, r_{in}, th$ be the outside radius, inside radius, and thickness respectively.

Thickness is by:
$th = r_{out} - r_{in}$

The volume is given by (volume of outside minus inside):
$\mathit{Vol} = \pi r_{out}^2h - \pi r_{in}^2h = \pi h(r_{out}^2 - r_{in}^2)$.

See what you did wrong?

3. But why

$\mathit{Vol} = \pi r_{out}^2h - \pi r_{in}^2h$

Volume is the capacity inside the cylindrical pipe..........

4. Hello, rn5a!

snowtea is absolutely correct . . .

But why?

$\mathit{Vol} = \pi r_{out}^2h - \pi r_{in}^2h$

Volume is the capacity inside the cylindrical pipe. . . . . no

"Volume" refers to the amount of material used to make the pipe,
. . not its "empty space".

5. Originally Posted by rn5a
But why

$\mathit{Vol} = \pi r_{out}^2h - \pi r_{in}^2h$

Volume is the capacity inside the cylindrical pipe..........
Well, this is your problem. Are you told specifically that the "volume" given refers to the inner capacity of the pipe? the interpretation of snowtea and Soroban, that the volume is the volume of material making up the pipe seems more reasonable to me- especially since by your interpretation, the outer radius is irrelevant. If we call the inner radius "r" then the inner volume of the pipe is just $\pi r^2h= 14\pi r^2= 748$. From that, $r^2= \frac{748}{(3.1416)(14)}= 17.0$ so that $r= \sqrt{17.0)= 4.12$ inches.