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Math Help - Volume of a Solid ?

  1. #1
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    Volume of a Solid ?

    Find the volume of the solid generated by revolving around the x-axis
    the region bounded by the x-axis, and one arch of the cycloid
    x = t−sint, y = 1−cost.
    where 0 ≤ t ≤ 2pi.
    [ Hint : Use the disk method and dV = piy2dx = piy2(dx/dt) dt ]

    I'm confused on this problem. I think it's because I don't actually know what they're asking... Is y the upper and x (t-sint) the width?
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  2. #2
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    Quote Originally Posted by maxreality View Post
    Find the volume of the solid generated by revolving around the x-axis
    the region bounded by the x-axis, and one arch of the cycloid
    x = t−sint, y = 1−cost.
    where 0 ≤ t ≤ 2pi.
    [ Hint : Use the disk method and dV = piy2dx = piy2(dx/dt) dt ]

    I'm confused on this problem. I think it's because I don't actually know what they're asking... Is y the upper and x (t-sint) the width?
    dV = \pi y^2 \, dx is the volume of a representative disk in terms of y and x.

    dV = \pi y^2 \cdot \frac{dx}{dt} \, dt = \pi(1-\cos{t})^2 \cdot (1-\cos{t}) \, dt is the same thing in terms of t since y and x are given in terms of t

    V = \pi \int_0^{2\pi} (1-\cos{t})^3 \, dt<br />
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