Chapter 6, Problem 66RE

Surface area and volume Let $f(x)=\frac{1}{3}{x}^3$ and let R be the region bounded by the graph of f and the x-axis on the interval [0, 2].

1. a. Find the area of the surface generated when the graph of f on [0, 2] is revolved about the x-axis.
2. b. Find the volume of the solid generated when R is revolved about the y-axis.
3. c. Find the volume of the solid generated when R is revolved about the x-axis.