Volumes Using the Disc Method

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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Related Curriculum Standards

US Common Core State Standards, Mathematics