Worksheet: Disc Method for Rotating around a Vertical

In this worksheet, we will practice finding the volume of a solid by revolution of a two-dimensional region about the y-axis using the disk method.

Q1:

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

• A
• B
• C81
• D
• E

Q2:

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 .

• A cubic units
• B3 cubic units
• C27 cubic units
• D cubic units

Q3:

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

Q4:

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

• A74 cubic units
• B cubic units
• C cubic units
• D cubic units

Q5:

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

Q6:

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

• A
• B128
• C256
• D
• E

Q7:

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 .

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

Q8:

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

Q9:

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