Today I reviewed how to calculate volumes of solids. You use different methods depending on the situation/problem that you are given (disk, washer, and shell methods).
Disk:
*You use this method when a solid is created by rotating an area around a given line.
Formula- Integral from a to b of (pi * r^2)dr.
Washer:
*You use this method when trying to calculate the volume of a solid with a known cross-section.
Formula- v = (the integral from a to b) of A(x)dx.
Shell:
*You use this method when you revolve the object around the y-axis.
Formula- v = 2 (pi) * (the integral from a to b) of p(x)h(x)dx.
*p = the distance from the center of the rectangle to the axis of revolution.
*h = the height of the rectangle.
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