Another equation

**earachefl** · July 10th 2007, 02:10 PM

Here's another one I'm having problems with. The equation given is

$S = \pi r\sqrt{r^2 + h^2}$

and you are supposed to solve for h.

I attacked it by

$S^2 = \pi^2r^2(r^2 + h^2)$
then
$\frac{S^2}{\pi^2r^2} = r^2 +h^2$
then
$\frac{S^2}{\pi^2r^2}-r^2=h^2$
and finally
$h = \pm\sqrt{\frac{S^2}{\pi^2r^2}-r^2}$

The book gives the answer as

$h = \frac {\sqrt{S^2 -\pi^2 r^4}} {\pi r}$

Am I on the right track but need to complete more steps to get to this?

**janvdl** · July 10th 2007, 02:13 PM

Originally Posted by earachefl

$h = \pm\sqrt{\frac{S^2}{\pi^2r^2}-r^2}$

The book gives the answer as

$h = \frac {\sqrt{S^2 -\pi^2 r^4}} {\pi r}$

Am I on the right track but need to complete more steps to get to this?

You should multiply the $r^2$ with $\frac{\pi^2r^2}{\pi^2r^2}$

And then you can take the square root of the numerator.

You were nearly there, good job!

**earachefl** · July 10th 2007, 02:19 PM

I'm sorry, I should multiply which 'r'?

**red_dog** · July 10th 2007, 02:19 PM

Originally Posted by earachefl

Am I on the right track but need to complete more steps to get to this?

Yes, you have to amplify $r^2$ with the denominator of the fraction.
Also, probably $h$ is a positive number (maybe the altitude of a figure).

**janvdl** · July 10th 2007, 02:20 PM

Originally Posted by earachefl

I'm sorry, I should multiply which 'r'?

The $r^2$ under the root.

**janvdl** · July 10th 2007, 02:22 PM

Originally Posted by red_dog

Also, probably $h$ is a positive number (maybe the altitude of a figure).

I agree, I only gave it a quick glance, so I'm not too sure, but it looks like the volume of a cylinder to me...

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