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# Volume of Solids of Revolution

For the following problem, sketch the region and then find the volume of the solid where the base is the given region and which has the property that each cross-section perpendicular to the x-axis is a semicircle.

1) the region bounded above by y=cosx, below by y=sinx and on the left by the y-axis

For the following problem, find the volume of the solid formed when the region described is revolved about the x-axis using washers or disks.

1) the region bounded by the lines x=0, x=1, y=x+1, and y=x+2

For the following problem, use shell to find the volume of the solid formed by revolving the given region about the y-axis.

1) the region bounded by the curve y= , the y-axis and the line y=1.
2) The region inside the ellipse about the y-axis.

#### Solution Summary

In the following posting, volumes of solids of revolution are found using the disk and shell methods. Step by step solutions are given with diagrams included.

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