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Math Help - volume

  1. #1
    Junior Member
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    volume

    How to find the solid generated by revolving a loop of the curve r^2=a^2sin2 \theta about the initial line.

    Here I used the fact that the volume

    V=\frac{2}{3}\int(f(\theta))^3sin\theta d\theta.


    But I couldn't get the answer. The answer should be \frac{{\pi}^2 a^3}{8}
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  2. #2
    Eater of Worlds
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    Did you try the Theorem of Pappus?. That may be a good choice here.

    Find the area of the region multiplied by the distance traveled by the centroid, then multiply by 2Pi
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