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