Wednesday, March 28, 2012

AP Calculus AB: Revolving Solids Known Cross Sections

This is a problem concerning the volume of a solid with known cross section. The calculation of the volume is found in three steps:

1) Express the area of the cross section as a function of a variable
2) Find the limits of integration
3) Integrate the function

The cross section can be a triangle, a square, rectangle, washer, etc. A washer has the shape of a disk with a circular region cut out from its center. Its area is found by subtracting the area of the inner circle from the area of the bigger circle.

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