# Worksheet: Volumes of Solids of Revolution Using the Disk and Washer Methods

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
• C
• D
• E186

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
• C
• D
• E25

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.

• A cubic units
• B9 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.

• A cubic units
• B cubic units
• C cubic units
• D14 cubic units

Q19:

Which of the following has a volume of ?

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

Q22:

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

• A
• B
• C
• D
• E

Q23:

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

• A
• B
• C
• D
• E

Q24:

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

• A3 cubic units
• B cubic units
• C cubic units
• D27 cubic units

Q25:

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