Approximating Volumes by Summation

The volume of a solid shape can be approximated by slicing it into layers and summing the volumes of all of the layers. The limit of this process is an integral that yields the volume of the solid. This is an analogue of a Riemann summation of the area under a curve.


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A Steinmetz solid, or a bicylinder, is the shape formed when two cylinders intersect at right angles.
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Related Curriculum Standards

US Common Core State Standards, Mathematics