# Volumes of Solids of Revolution and Sketches of Bounded Regions

Sketch the given region and then find the volume of the solid whose base is the given region and which has the property that each cross section perpendicular to the x-axis is a square.

2) the region bounded by the x-axis and the semi circle y = SQRT (16-x^2).

Sketch the given region and then find the volume of the solid whose base is the given region and which has the property that each cross section perpendicular to the x-axis is an equilateral triangle.

6) the region bounded by the curves y=x^3 and y=x^2.

Sketch the given region and then find the volume of the solid whose base is the given region and which has the property that each cross section perpendicular to the x-axis is a semicircle.

10) the region bounded by y=cosx, below by y=sinx, and on the left by the y axis.

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#### Solution Summary

Volumes of solids of revolution and sketches of bounded regions are investigated and discussed. The solution is detailed and well presented.