# Worksheet: Volumes

Q1:

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
• D13 cubic units
• E cubic units

Q2:

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
• B cubic units
• C cubic units
• D170 cubic units

Q3:

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

Q4:

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
• D3 cubic units
• E cubic units

Q5:

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

• A cubic units
• B cubic units
• C cubic units
• D30 cubic units

Q6:

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.

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:

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

Q9:

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.

• A volume units
• B volume units
• C volume units
• D volume units

Q10:

The region bounded by the curves , , and is rotated about the -axis. Find the volume of the resulting solid.

• A
• B9
• C
• D
• E

Q11:

Let and be constants. Find the volume of the solid of revolution produced on turning the region bounded by the curve and the -axis about the -axis.

• A
• B
• C
• D

Q12:

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

Q13:

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

Q14:

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

• A
• B
• C
• D
• E