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Worksheet: Finding the Volume of a Solid of Revolution about the y-Axis Using the Washer Method

Q1:

Find the volume of the solid obtained by rotating the region bounded by the curves π‘₯ = 6 βˆ’ 5 𝑦 2 and π‘₯ = 𝑦 4 about the 𝑦 -axis.

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

Q2:

Find the volume of the solid obtained by rotating the region bounded by the curves π‘₯ = 6 βˆ’ 3 𝑦 2 and π‘₯ = 3 𝑦 4 about the 𝑦 -axis.

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

Q3:

Find the volume of the solid obtained by rotating the region bounded by the curve 𝑦 = π‘₯ 2 and the line π‘₯ = 3 𝑦 about the 𝑦 -axis.

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

Q4:

Find the volume of the solid obtained by rotating the region bounded by the curve 3 𝑦 = π‘₯ 2 and the line π‘₯ = 3 𝑦 about the 𝑦 -axis.

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

Q5:

Find the volume of the solid generated by rotating the region bounded by the curve 𝑦 = 3 βˆ’ π‘₯ 2 and the straight line π‘₯ = 2 a complete revolution about the 𝑦 -axis.

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

Q6:

Find the volume of the solid generated by rotating the region bounded by the curve 3 𝑦 = 5 βˆ’ π‘₯ 2 and the straight line π‘₯ = 2 a complete revolution about the 𝑦 -axis.

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

Q7:

Find the volume of the solid obtained by rotating the region bounded by the curve 5 π‘₯ = 𝑦 2 and the lines π‘₯ = 0 and 𝑦 = 2 about the 𝑦 -axis.

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

Q8:

Find the volume of the solid obtained by rotating the region bounded by the curve 5 π‘₯ = 2 𝑦 2 and the lines π‘₯ = 0 and 𝑦 = 5 about the 𝑦 -axis.

  • A 2 0 0 πœ‹
  • B100
  • C200
  • D 1 0 0 πœ‹
  • E 5 0 πœ‹ 3