# Worksheet: Volumes of Solids of Revolution Using the Shell Method

In this worksheet, we will practice finding the volume of a solid generated by revolving an area around a vertical or horizontal axis using the shell method.

**Q1: **

Find the volume of the solid obtained by rotating the region bounded by the curves , , , and about .

- A
- B
- C
- D
- E

**Q2: **

Consider the region bounded by the curve and lines , , and . Find the volume of the solid obtained by rotating this region about . Round your answer to two decimal places.

**Q3: **

Consider the region in the half plane bounded by the curves and . Find the volume of the solid obtained by rotating this region about -axis. Round your answer to two decimal places.

**Q4: **

Calculate the volume of a solid generated by rotating the region bounded by the curve and straight lines and a complete revolution about the -axis.

- A volume units
- B volume units
- C volume units
- D volume units

**Q5: **

Calculate the volume of a solid generated by rotating the region bounded by the curve , the -axis, and the straight line a complete revolution about the -axis.

- A117 volume units
- B volume units
- C volume units
- D volume units

**Q6: **

Find the volume of the solid obtained by rotating the region bounded by the curve and the lines and about the line .

- A
- B
- C
- D
- E

**Q9: **

Find the volume of the solid generated by turning the region bounded by the curves , , and a complete revolution about the -axis.

- A18 cubic units
- B cubic units
- C72 cubic units
- D cubic units

**Q10: **

Find the volume of the solid generated by turning the region bounded by the curves , , , and the -axis through a complete revolution about the -axis.

- A cubic units
- B cubic units
- C cubic units
- D cubic units

**Q11: **

Find the volume of the solid generated by revolving the region bounded by the curve and the straight lines and a complete revolution about the -axis.

- A cubic units
- B cubic units
- C cubic units
- D cubic units
- E cubic units