Results 1 to 1 of 1

Math Help - Optimization; cylinder inside sphere

  1. #1
    Junior Member Tclack's Avatar
    Joined
    Oct 2009
    From
    No permanant location.
    Posts
    57
    Thanks
    1

    Optimization; cylinder inside sphere

    Find the dimensions(r and h) of the right circular cylinder of greatest Surface Area that can be inscribed in a sphere of radius R.

    my work so far

     SA=2\pi r^2+2\pi rh

    r^2 + (\frac{h}{2})^2 = R^2

    h=2\sqrt{R^2-r^2}

     SA=2\pi r^2+4\pi r\sqrt{R^2-r^2}

     \frac{dSA}{dr}=4\pi r+4\pi (\sqrt{R^2-r^2}+\frac{-2r^2}{2\sqrt{R^2-r^2}})

    I tried setting that equal to zero, but I wasn't coming up with the right answer

    The answer in the book(not mine): r=\sqrt{\frac{5+\sqrt{5}}{10}}R
    h=2\sqrt{\frac{5-\sqrt{5}}{10}}R

    Can anyone see my error, or did I make one?
    Last edited by Tclack; October 13th 2009 at 03:54 PM. Reason: clarification
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: November 16th 2011, 09:11 AM
  2. Area of a surface inside a cylinder
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 26th 2010, 03:05 PM
  3. Volume inside a sphere and outside a cylinder
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 22nd 2010, 04:37 AM
  4. Replies: 17
    Last Post: June 14th 2009, 05:30 PM
  5. Fitting a cylinder inside a cone
    Posted in the Geometry Forum
    Replies: 3
    Last Post: March 19th 2009, 01:37 PM

Search Tags


/mathhelpforum @mathhelpforum