Results 1 to 5 of 5

Thread: Volum of a cylinder in a cone (driving me insane!)

  1. #1
    Junior Member
    Joined
    Apr 2010
    From
    Australia
    Posts
    26

    Volum of a cylinder in a cone (driving me insane!)

    a cylinder of radius r and height h is inscribed within a cone with bas radius 6 and height 20

    1) show that the volume of the cylinder is given by

    V= 10.(pi).r^2.(6-r)
    --
    3

    2) find r and h

    3) what is the maximum volume
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Unknown008's Avatar
    Joined
    May 2010
    From
    Mauritius
    Posts
    1,260
    Thanks
    1
    First, what is the relationship between the height of the cylinder and the radius of the cylinder?

    If you make a sketch, you'll see that for a certain radius r, the cone would have a height of l = (r/6)*20, using similar triangles.



    From here, the height of the cylinder will become h = 20 - (20r)/6.

    Then, the formula for the volume of a cylinder is

    V = \pi r^2 h

    Using the equation you got, you now get:

    V = \pi r^2 (20 - \frac{20r}{6})

    Simplifying;

    V = \frac{10}{3}\pi r^2 (6-r)

    For the second part, are you sure that's the question? Because r and h would vary, depending on the volume. If the question was in fact, "Find the value of r and h, provided that the volume of the cylinder is maximised." there there would be a solution.
    Last edited by Unknown008; Aug 14th 2010 at 08:47 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Apr 2010
    From
    Australia
    Posts
    26
    thanks. it says to find h and r when they are maximum values so i think i shouldve posted this in calculus
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Unknown008's Avatar
    Joined
    May 2010
    From
    Mauritius
    Posts
    1,260
    Thanks
    1
    Yes, you need to find the derivative of V, and solve for V' at V' = 0.

    You will get the radius in this situation, and you can then find the height using r.
    Last edited by Unknown008; Aug 14th 2010 at 09:47 PM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Apr 2010
    From
    Australia
    Posts
    26
    ok thanks
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. optimization - cylinder in cone
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Feb 4th 2010, 09:20 PM
  2. a cylinder is inscribed in a cone
    Posted in the Geometry Forum
    Replies: 1
    Last Post: Mar 16th 2009, 10:23 PM
  3. Please help me...this is driving me insane
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Aug 27th 2008, 03:54 PM
  4. Cylinder in a Cone
    Posted in the Geometry Forum
    Replies: 2
    Last Post: Jan 24th 2007, 12:59 PM
  5. Cylinder and Cone
    Posted in the Calculus Forum
    Replies: 7
    Last Post: Apr 13th 2006, 07:50 AM

Search Tags


/mathhelpforum @mathhelpforum