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What is the volume of the solid revolution?

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The region in the first quadrant bounded by the graphs of y = x and y = x^2/2 is rotated around the line y=x. Find (a) the centroid of the region and (b) the volume of the solid of revolution.

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Solution Summary

This shows how to find centroid and volume of a solid of revolution.

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Calculus Finding Volume of the solid of revolution obtained by rotating a region.

Question (1)
What is the volume of the solid of revolution obtained by rotating the region bounded by y = 1 and y = 5 - x^2 around the X-axis.

Question (2)
Find the volume of the solid of revolution obtained by rotating the region bounded by y = 1 and y = Tan x about the x-axis from x = 0 to x = pi/4.

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