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Surface area, volume, work

Find the area of the surface obtained when the graph of y = x2, 0 ≤ x ≤ 1, is rotated around the y-axis.

Find the volume of the solid that is generated by rotating the region formed by the graphs of y = x2, y = 2, and x = 0 about the y-axis.

A 100-ft length of steel chain weighing 15 lb/ft is hanging from the top of a tall building. How much work is done in pulling all of the chain to the top of the building?

Solution Summary

These are three calculus problems involving surface area, volume, and work.