In this worksheet, we will practice finding the volume of a solid generated by revolving a region around either a horizontal or a vertical line using the disk and washer methods.

**Q1: **

Consider the region bounded by the curves , , , and . Determine the volume of the solid of revolution created by rotating this region about the -axis.

- A
- B93
- C186
- D
- E

**Q2: **

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

- A
- B
- C25
- D
- E

**Q3: **

Consider the region bounded by the curve and the lines , , and . Set up an integral for the volume of the solid obtained by rotating this region about the -axis.

- A
- B
- C
- D
- E

**Q4: **

Consider the region bounded by the curve and the lines , , and . Set up an integral for the volume of the solid obtained by rotating this region about the -axis.

- A
- B
- C
- D
- E

**Q5: **

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

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

**Q6: **

Find the volume of the solid obtained by rotating the region bounded by the curves and about where . Give your answer to two decimal places.

**Q7: **

Consider the region bounded by the curve and the lines , , and . Set up an integral for the volume of the solid obtained by rotating that region about .

- A
- B
- C
- D
- E

**Q8: **

Set up an integral for the volume of the solid obtained by rotating the region bounded by the curve and the lines , , and about .

- A
- B
- C
- D
- E

**Q9: **

Consider the region between the curves and , for . Find the volume of the solid of revolution obtained by rotating this region about the -axis, giving your answer to two decimal places.

**Q10: **

Find the volume of the solid obtained by rotating the region bounded by the curves , , , and about . Give your answer to two decimal places.

**Q11: **

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

- A
- B
- C
- D
- E

**Q12: **

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

**Q13: **

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

- A
- B
- C
- D
- E

**Q14: **

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

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

**Q15: **

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

- A9 cubic units
- B cubic units
- C cubic units
- D cubic units

**Q16: **

Determine, to two decimal places, the volume of the solid obtained by rotating the region bounded by the curve and the lines , , and about the -axis.

**Q17: **

Set up an integral for the volume of the solid obtained by rotating the region bounded by the curve about .

- A
- B
- C
- D
- E

**Q18: **

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

- A14 cubic units
- B cubic units
- C cubic units
- D cubic units

**Q19: **

Which of the following has a volume of ?

- Aa right circular cone whose height is 15 units
- Ba sphere whose radius length is 25 units
- Ca sphere whose radius length is 5 units
- Da right circular cylinder whose height is 15 units
- Ea right circular cylinder whose height is 5 units

**Q20: **

Determine, to two decimal places, the volume of the solid obtained by rotating the region bounded by the curves and about .

**Q21: **

Set up an integral for the volume of the solid obtained by rotating the region bounded by the curve about .

- A
- B
- C
- D
- E