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Math Help - Optimization - Cylinder inscribed in Cone

  1. #1
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    Optimization - Cylinder inscribed in Cone

    Find the largest total surface area (including top and bottom) of a cylinder inscribed in a cone of base radius 9 and height 21.
    We need to maximize the following function and :

    Then we solve for in terms of obtaining:

    We thus obtain the following formula for in terms of alone:

    varies over the interval , where


    has one stationary point at:

    We conclude that the maximum possible total surface area of such a cylinder is:


    I know that the surface area is S=2pir(r+h)
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  2. #2
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    i feel like if i can get the relation of h and r i will be good to go
    i tried doing this by setting 9/r=21/h and getting r=9h/21 however the computer is telling me that this is wrong
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