Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.

Lesson: Finding Volume of a Solid by Rotating around a Vertical Line Using the Shell Method

Worksheet: Finding Volume of a Solid by Rotating around a Vertical Line Using the Shell Method • 13 Questions

Q1:

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 .

  • A27 cubic units
  • B cubic units
  • C cubic units
  • D3 cubic units

Q2:

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

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:

Find the volume of the solid generated by rotating 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
  • E cubic 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.

  • A volume units
  • B volume units
  • C117 volume units
  • D volume units

Q6:

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

Q7:

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
  • E

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:

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

  • A
  • B
  • C
  • D
  • E

Q10:

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

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:

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

Q13:

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.

Preview