# 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

Q7:

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

• A cubic units
• B cubic units
• C cubic units
• D cubic units

Q8:

Consider the region bounded by the curves and , for . Find the volume of the solid obtained by rotating this region about the -axis.

• 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