Surfaces of revolution are formed when a shape outlined in the x-y plane of the Cartesian coordinate system is revolved 360° around an axis of revolution to form a 3-dimensional figure. The original shape can be described mathematically in various ways. It can be defined by a single equation bordered by x and y coordinates, for example, the shape shown in Figure 1 is the area bounded by a line and the x and y-axis. Revolving this 2-dimensional triangle around the x-axis provides the 3-dimensional cone shown in Figure 2.

A semi-circle, centered at the origin, and bounded by the y-axis is shown in Figure 3. Revolving this semi-circle around the y-axis provides the sphere shown in Figure 4. A circle centered at (x,y) coordinates of (5,5) is shown in Figure 5. Revolution of this circle around the y-axis provides the doughnut-shaped torus shown in...