Results 1 to 2 of 2

Math Help - a cylinder is inscribed in a cone

  1. #1
    Newbie
    Joined
    Mar 2009
    Posts
    2

    a cylinder is inscribed in a cone

    A cylinder is inscribed in a cone. The cylinder has an altitude of 15 cm and a radius of 3 cm. Express H as a function of R.

    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,811
    Thanks
    701
    Hello, katinthehat108!

    I think I know what you meant . . .


    A cylinder is inscribed in a cone.
    The cylinder has an altitude of 15 cm and a radius of 3 cm.
    Express H (height of the cone) as a function of R (radius of the cone).
    Code:
        -           *           -
        :          /|\          :
        :         / |:\        H-15
        :        /  |::\        :
        :       *---+---*       -
        H      /|   | 3 |\      :
        :     / |   |   |:\    15
        :    /  |   | 15|::\    :
        :   /   |   |   |:::\   :
        :  /    |   |   |::::\  :
        - *-----*---+---*-----* -
                    : 3 : R-3 :
                    : -- R -- :

    The two shaded triangles are similar.

    Hence, we have: . \frac{H-15}{3} \:=\:\frac{15}{R-3} \quad\Rightarrow\quad (H-15)(R-3) \:=\:45

    . . . . HR - 3H - 15R + 45 \:=\:45 \quad\Rightarrow\quad HR - 3H \:=\:15R

    . . . . H(R-3) \:=\:15R \quad\Rightarrow\quad\boxed{ H \:=\:\frac{15R}{R-3}}

    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: February 7th 2011, 01:47 PM
  2. Optimization - Cylinder inscribed in Cone
    Posted in the Calculus Forum
    Replies: 1
    Last Post: November 17th 2010, 11:10 AM
  3. Replies: 8
    Last Post: September 7th 2010, 05:37 AM
  4. Cylinder inscribed in a Cone Optimization
    Posted in the Calculus Forum
    Replies: 1
    Last Post: March 18th 2009, 05:35 AM
  5. Replies: 2
    Last Post: February 12th 2007, 05:22 AM

Search Tags


/mathhelpforum @mathhelpforum