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calculus

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A right triangle with hypotenuse 5 inches is revolved around one of its legs to generate a right circular cone. Find the radius and height of the greatest volume cone.

  • calculus -

    v = 1/3 pi r^2 h

    r^2 + h^2 = 25

    v = 1/3 pi (25-h^2)h = 1/3 pi (25h - h^3)

    a max/min occurs when dv/dh = 0:

    25 - 3h^2 = 0
    h = 5/√3
    r = 5√2/√3

    It's a max because v'' < 0

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