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Math Help - Find the volume of the solid

  1. #1
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    Arrow Find the volume of the solid

    Find the volume of the solid whose base is the region between the curve y=x^3 and y-axis from y=0 to y=1, and whose cross sections taken perpendicular to the y-axis are squares.

    I don't understand "whose cross sections taken perpendicular to y-axis are squares".

    How can I solve this problem? If possible, would you please explain step by step?

    Thank you very much.
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  2. #2
    Eater of Worlds
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    Picture a bunch of squares stacked up perp.to the y-axis in your given region.

    This is NOT a volume of revolution. Since we are perp to the y-axis we will integrate wrt y.

    x=y^{\frac{1}{3}}

    The area of a square is x^{2}

    So, we have \int_{0}^{1}y^{\frac{2}{3}}dy
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