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Worksheet: Calculating Volumes of Solids of Revolution

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.

  • A13 cubic units
  • B cubic units
  • C cubic units
  • D 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
  • B170 cubic units
  • C cubic units
  • D 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 turning the region bounded by the curves , , and a complete revolution about the -axis.

  • A cubic units
  • B30 cubic units
  • C cubic units
  • D cubic units

Q5:

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.

Q6:

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

Q7:

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

Q8:

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

Q9:

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

  • A
  • B
  • C9
  • D
  • E

Q10:

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

Q11:

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

Q12:

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

Q13:

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

  • A
  • B
  • C
  • D
  • E