Exercises for the disk and washer methods.

The region with , shown below, is revolved around the -axis. Use the disk method to find the volume of the solid of revolution.

The radius will be a difference of -values because slices are indexed by the variable . Each slice will extend from to , and so must be the larger of these -values minus the smaller of these -values.
The region with , shown below, is revolved around the axis . Use the disk method to find the volume of the solid of revolution.

The radius will be a difference of -values because slices are indexed by the variable . Each slice will extend from to , and so must be the larger of these -values minus the smaller of these -values
The region with , shown below, is revolved around the axis . Use the washer method to find the volume of the solid of revolution.

Each radius will be a difference of -values because slices are indexed by the variable . The distance from the axis to the line is , and the distance from the axis to is .
The region with , shown below, is revolved around the axis . Use the washer method to find the volume of the solid of revolution.

Each radius will be a difference of -values because slices are indexed by the variable . The distance from the axis to the line is , and the distance from the axis to is .

Sample Quiz Questions

The region in the plane bounded on the left by the curve , on the right by the curve , above by the line , and below by the line is revolved around the axis . Compute the volume of the resulting solid. (Hints won’t reveal until after you choose a response.)

The region in the plane bounded below by the curve , above by the curve , on the right by the line , and on the left by the line is revolved around the axis . Compute the volume of the resulting solid. (Hints won’t reveal until after you choose a response.)

The region in the plane given by and is revolved around the -axis. Compute the volume of the resulting solid. (Hints won’t reveal until after you choose a response.)