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The Riemann sums used for calculating the area under a curve use approximating rectangles. To calculate the volume of solids of revolution, cylinders are the approximating elements. If the area of a cross section near the point ... is ... and the thickness of the cylinder is ... , its volume is ... . The radius of the solid of revolution of the function ... at ... is ... so ... . In terms of Riemann sums and integrals the volume is ... , where ... .
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