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    The answer to Volume of solids

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    1. Find the volume of the solid formed by rotating the ellipse (x/a)^2 + (y/b)^2 = 1 about the x axis.

    12. The base of a solid is the region bounded by the parabola y = x^2 / 2 and the line y = 2. Each plane section of the solid perpendicular to the y axis is an equilateral triangle. Find the volume of the solid.

    17. Find the volume of the sphere by integrating from y = -r to y = r . Compare the result with the one arrived at by taking twice the integral from y = 0 to y = r.

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    The expert finds the volume of solids in this case.