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Lesson: Finding Volume of a Solid by Rotating around x-axis Using Disk Method

In this lesson, we will learn how to find the volume of a solid by revolution of a two-dimensional region about the x-axis using the disk method.

Worksheet: Finding Volume of a Solid by Rotating around x-axis Using Disk Method • 14 Questions

Q1:

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

Q2:

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

  • A
  • B25
  • C
  • D
  • E

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:

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

Q6:

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

Q7:

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.

Q8:

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
  • B186
  • C
  • D
  • E93

Q9:

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
  • C9 cubic units
  • D cubic units

Q10:

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
  • D122 cubic units

Q11:

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
  • C8 cubic units
  • D cubic units

Q12:

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

Q13:

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

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
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