1. ## Another equation

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

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

and you are supposed to solve for h.

I attacked it by

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

The book gives the answer as

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

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

2. Originally Posted by earachefl
$\displaystyle h = \pm\sqrt{\frac{S^2}{\pi^2r^2}-r^2}$

The book gives the answer as

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

Am I on the right track but need to complete more steps to get to this?
You should multiply the $\displaystyle r^2$ with $\displaystyle \frac{\pi^2r^2}{\pi^2r^2}$

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

You were nearly there, good job!

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

4. 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 $\displaystyle r^2$ with the denominator of the fraction.
Also, probably $\displaystyle h$ is a positive number (maybe the altitude of a figure).

5. Originally Posted by earachefl
I'm sorry, I should multiply which 'r'?
The $\displaystyle r^2$ under the root.

6. Originally Posted by red_dog
Also, probably $\displaystyle h$ 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...