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March 27, 2017

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The region between the graphs of x=y^2 and x=4y is rotated around the line y=4.
The volume of the resulting solid is?

  • Calculus - ,

    I assume you made a sketch.
    You should have the two graphs intersecting at (0.0) and (16,4)

    So we will washer discs with outer ratius of 4 - x/4 and inner radius of 4 - √x

    area of washer disc = π(4-x/4)^2 = π(4-√x)^2
    = π(16 - 2x + x^2/4 - (16 - 8√x + x)
    = π( -3x + x^2 + 8x^(1/2)

    volume = π∫(-3x + x^2 + 8x^(1/2) dx from 0 to 16
    = π [ (-3/2)x^2 + (1/3)x^3 + (16/3)x^(3/2) ] from 0 to 16

    = π(-384 + 4096/3 + 1024/3 - 0]
    = π(3968/3)

    check my arithmetic

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