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calculus

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A ball of radius 10 has a round hole of radius 8 drilled through its center. Find the volume of the resulting solid.

  • calculus -

    whole ball = 4/3(pi)(10^3)= (4000/3)(pi)

    now drill out the integral of Pi(y^2)dx from -4 to 4 or
    2pi(integral)(100-x^2)dx from 0 to 4
    = 2pi [ 100x - (1/3)x^3] from 0 to 4
    = 2pi(400 - 64/3]
    = 2pi(1136/3)

    so the volume of the solid is
    4000pi/3 - 2275pi/3 = 1728pi/3

    please check my arithmetic.

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