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March 29, 2017

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A right circular cone has a fixed slant height, s= 12 inches. Determine the radius and the height of the cone with maximum volume

  • ap Calculus - ,

    volume of cone is

    V=4/3(pi)r^2h

    s^2=r^2+h^2 or s^2-h^2=r^2

    V=4/3(pi)(s^2-h^2)h

    if 4/3(pi)=k

    V=k(144-h^2)h

    V=144kh-kh^3

    volume is a max when dV/dh is zero

    dV/dh = 144k-3kh^2

    144k-3kh^2 = 0

    144k = 3kh^2
    48=h^2

    this gives you h, from which you can find r from

    s^2-h^2=r^2

    please check my maths!

  • ap Calculus - ,

    I am sure that Dr Russ meant to type

    volume of cone is

    V=1/3(pi)r^2h

  • ap Calculus - ,

    Yes oops!

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