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Lesson: Shell Method for Rotating around a Vertical

Worksheet • 6 Questions

Q1:

Find the volume of the solid obtained by rotating the region bounded by the curves 5 𝑦 = π‘₯ , 𝑦 = 0 , π‘₯ = 3 , and π‘₯ = 4 about π‘₯ = 2 .

  • A 3 2 πœ‹ 1 5
  • B 7 πœ‹ 1 0
  • C πœ‹ 3
  • D 2 πœ‹ 3
  • E 6 4 πœ‹ 1 5

Q2:

Calculate the volume of a solid generated by rotating the region bounded by the curve 𝑦 = 5 π‘₯ βˆ’ 2 2 , the 𝑦 -axis, and the straight line 𝑦 = 1 a complete revolution about the 𝑦 -axis.

  • A 9 πœ‹ 1 0 volume units
  • B 9 1 0 volume units
  • C 1 1 7 πœ‹ volume units
  • D117 volume units

Q3:

Calculate the volume of a solid generated by rotating the region bounded by the curve 𝑦 = 2 βˆ’ 7 π‘₯ 2 and straight lines π‘₯ = 1 and 𝑦 = 4 a complete revolution about the 𝑦 -axis.

  • A 4 5 πœ‹ 1 4 volume units
  • B 4 5 1 4 volume units
  • C 4 5 πœ‹ 7 volume units
  • D 4 5 7 volume units

Q4:

Consider the region bounded by the curve π‘₯ 𝑦 = 4 and lines 𝑦 = 0 , π‘₯ = 1 , and π‘₯ = 2 . Find the volume of the solid obtained by rotating this region about π‘₯ = βˆ’ 5 . Round your answer to two decimal places.

Q5:

Consider the region in the half plane 𝑦 β‰₯ 0 bounded by the curves 𝑦 = 4 π‘₯ 2 and π‘₯ + 𝑦 = 7 2 2 . Find the volume of the solid obtained by rotating this region about 𝑦 -axis. Round your answer to two decimal places.

Q6:

Set up an integral for the volume of the solid obtained by rotating the region bounded by the curve 4 π‘₯ + 𝑦 = 4 2 2 about π‘₯ = 2 .

  • A 1 6 πœ‹ ο„Έ ο„ž 1 βˆ’ 𝑦 4 𝑦 2 0 2 d
  • B 8 ο„Έ ο„ž 1 βˆ’ 𝑦 4 𝑦 2 0 2 d
  • C 8 πœ‹ ο„Έ ο„ž 1 βˆ’ 𝑦 4 𝑦 2 0 2 d
  • D 4 πœ‹ ο„Έ ο„ž 1 βˆ’ 𝑦 4 𝑦 2 0 2 d
  • E 1 6 ο„Έ ο„ž 1 βˆ’ 𝑦 4 𝑦 2 0 2 d
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