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Worksheet: Washer Method for Rotating around a Vertical

Q1:

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

  • A 9 6 πœ‹ 5
  • B 6 4 πœ‹ 5
  • C 1 2 8 πœ‹ 5
  • D 5 6 πœ‹ 5
  • E 1 1 2 πœ‹ 5

Q2:

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

  • A 4 9 6 πœ‹ 5
  • B 6 4 πœ‹ 5
  • C 1 2 8 πœ‹ 5
  • D 1 3 6 πœ‹ 5
  • E 2 7 2 πœ‹ 5

Q3:

Consider the region bounded by the curves 𝑦 = 8 π‘₯ 3 , 𝑦 = 0 , and π‘₯ = 1 . Find the volume of the solid obtained by rotating this region about π‘₯ = 5 .

  • A 7 2 4 πœ‹ 5
  • B 1 6 πœ‹ 5
  • C 3 2 πœ‹ 5
  • D 8 4 πœ‹ 5
  • E 1 6 8 πœ‹ 5

Q4:

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

  • A 2 5 6 πœ‹ 5
  • B 6 4 πœ‹ 5
  • C 1 2 8 πœ‹ 5
  • D 9 6 πœ‹ 5
  • E 1 9 2 πœ‹ 5