Results 1 to 4 of 4

Math Help - Find maximum size of Cylinder that fits in sphere

  1. #1
    Newbie
    Joined
    Sep 2009
    Posts
    19

    Find maximum size of Cylinder that fits in sphere

    I'm kinda stuck on this.

    I need to find the maximum size of a Cylinder that fits in sphere of radius 1.

    Ive come up with the following, .. am I on the right track so far?

    Volume of Cylinder = Pi(r^2)h = Pi(r^2)(sqrt(1^2 - r^2))
    Volume of Sphere = 4/3(Pi)(r^3)

    Pi(r^2)(sqrt(1^2 - r^2)) = 4/3(Pi)(r^3)

    Now I just need to solve for r. Is this correct? Where does the differentiation come into it?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,536
    Thanks
    1389
    Quote Originally Posted by floater View Post
    I'm kinda stuck on this.

    I need to find the maximum size of a Cylinder that fits in sphere of radius 1.

    Ive come up with the following, .. am I on the right track so far?

    Volume of Cylinder = Pi(r^2)h = Pi(r^2)(sqrt(1^2 - r^2))
    Volume of Sphere = 4/3(Pi)(r^3)
    You are good up to here.

    Pi(r^2)(sqrt(1^2 - r^2)) = 4/3(Pi)(r^3)
    No, the volume of the cylinder is not equal to the volume of a sphere. You have already used "fits inside a sphere of radius 1" to deduce that h= \sqrt{1- r^2}. Differentiate \pi r^2(1- r^2)^{1/2} and set the derivative equal to 0 to find the r that gives maximum volume.

    Now I just need to solve for r. Is this correct? Where does the differentiation come into it?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2009
    Posts
    19
    \pi r^2(1-r^2)^{1/2}

    Well i make the derivitive of the above to be :

    \pi2r(1-r^2)^{1/2} + r^2 1/2(1-r^2)^{-1/2}2r

    I dont know how i would factor that out. Could you give me some hints?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Sep 2009
    Posts
    19
    Am i right in thinking that i have to factor it first? Into something like


    ()() = 0

    ?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. cylinder in a sphere
    Posted in the Calculus Forum
    Replies: 1
    Last Post: October 14th 2010, 12:16 PM
  2. cylinder n sphere
    Posted in the Calculus Forum
    Replies: 2
    Last Post: August 10th 2010, 07:41 AM
  3. cylinder in a sphere
    Posted in the Geometry Forum
    Replies: 2
    Last Post: June 23rd 2009, 12:19 AM
  4. Cylinder in a Sphere
    Posted in the Geometry Forum
    Replies: 5
    Last Post: May 10th 2008, 04:16 PM
  5. Cylinder/Sphere
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 6th 2007, 08:01 PM

Search Tags


/mathhelpforum @mathhelpforum