THE DISK METHOD
To find the volume of a solid of revolution with the disk method, use one of the formulas below. (See Figure 7.15.)
Horizontal Axis of Revolution:
Volume = V = ∫[a,b] π[R(x)]^2 dx
Vertical Axis of Revolution:
Volume = V = ∫[c,d] π[R(y)]^2 dy
where R(x) or R(y) represents the radius of the disk at a given x or y value, respectively.
Figure 7.15: Horizontal axis of revolution, Vertical axis of revolution
Use the Disk Method to find the volume of the solid generated by revolving the region bounded by the graphs y = 3x, y = 0, and y = 3 about the x-axis.