Worksheet: Washer Method for Rotating around a Vertical

In this worksheet, we will practice finding the volume of a solid of a two-dimensional revolution region about a vertical line using the washer method.

Q1:

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

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

Q2:

Find the volume of the solid obtained by rotating the region bounded by the curve 𝑦 = 𝑥 and the line 𝑥 = 3 𝑦 about the 𝑦 -axis.

  • A 3 2 4 𝜋 5
  • B 2 4 3 𝜋 5
  • C 8 1 𝜋
  • D 1 6 2 𝜋 5
  • E 9 𝜋 2

Q3:

Find the volume of the solid obtained by rotating the region bounded by the curves 𝑥 = 6 5 𝑦 2 and 𝑥 = 𝑦 4 about the 𝑦 -axis.

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

Q4:

Find the volume of the solid generated by rotating the region bounded by the curve 𝑦 = 3 𝑥 2 and the straight line 𝑥 = 2 a complete revolution about the 𝑦 -axis.

  • A 𝜋 2 cubic units
  • B 1 2 cubic units
  • C 3 2 5 cubic units
  • D 3 2 𝜋 5 cubic units
  • E 7 2 𝜋 5 cubic units

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