Calculus

Calculate the height of a cylinder of maximum volume that can be cut from a cone of height 20 cm and base radius 80 cm ,

please help me

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  1. radius = r = 80 - (80/20)h
    r = 80 - 4 h

    v = pi r^2 h
    v = pi (80-4h)^2 h
    dv/dh = 0 for max or min
    0 = (80-4h)^2 + h (2)(80-4h)(-4)
    0 = 6400-640h+16h^2 - 640h+32h^2
    48h^2 - 1280 h + 6400 = 0
    6 h^2 - 160 h + 800 = 0
    3 h^2 - 80 h+ 400 = 0
    (3 h - 20 )(h - 20 ) = 0
    h = 30 (no good, minimum)
    or
    h = 20/3 approximately 7

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