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Calculus

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Find the volume of the solid formed by revolving the region bounded by the graphs of y=4x^2 and y=16 about the x-axis. (Washer Volume)

  • Calculus - ,

    integral from y = 0 to y = 16 (origin to x = 2)
    find volume of outer cylinder of radius 16
    Vol - pi r^2 h = pi (16^2) (2)

    find volume generated by inner curve between x axis and y = 4 x^2
    Vinner = pi y^2 dx from 0 to 2
    = pi 16 * integral x^4 dx
    = 16 pi (32/5)

    then subtract the inner from the outer
    2 pi (16^2) - 16 pi (32/5)

    = 32 pi *16 - 32 pi *16/5

    = 32 pi (4/5) (16)

  • Calculus - ,

    Oh, double that to include the left side.

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