Results 1 to 6 of 6

Thread: Another equation

  1. #1
    Junior Member
    Joined
    Jul 2007
    Posts
    43

    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?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Bar0n janvdl's Avatar
    Joined
    Apr 2007
    From
    Meh
    Posts
    1,630
    Thanks
    6
    Quote Originally Posted by earachefl View Post
    $\displaystyle h = \pm\sqrt{\frac{S^2}{\pi^2r^2}-r^2}$

    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!
    Last edited by janvdl; Jul 10th 2007 at 02:17 PM. Reason: My sloppy typing :D
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jul 2007
    Posts
    43
    I'm sorry, I should multiply which 'r'?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5
    Quote Originally Posted by earachefl View Post
    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).
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Bar0n janvdl's Avatar
    Joined
    Apr 2007
    From
    Meh
    Posts
    1,630
    Thanks
    6
    Quote Originally Posted by earachefl View Post
    I'm sorry, I should multiply which 'r'?
    The $\displaystyle r^2 $ under the root.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Bar0n janvdl's Avatar
    Joined
    Apr 2007
    From
    Meh
    Posts
    1,630
    Thanks
    6
    Quote Originally Posted by red_dog View Post
    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...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: Apr 11th 2011, 01:17 AM
  2. Partial differential equation-wave equation - dimensional analysis
    Posted in the Differential Equations Forum
    Replies: 3
    Last Post: Aug 28th 2009, 11:39 AM
  3. Replies: 2
    Last Post: May 18th 2009, 12:51 PM
  4. Replies: 2
    Last Post: Apr 28th 2009, 06:42 AM
  5. Replies: 1
    Last Post: Oct 23rd 2008, 03:39 AM

Search Tags


/mathhelpforum @mathhelpforum