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

Worksheet • 6 Questions

Q1:

Consider the region bounded by the curve 𝑦 = 5 𝑒 βˆ’ 2 π‘₯ 2 and the lines 𝑦 = 0 , π‘₯ = βˆ’ 4 , and π‘₯ = 4 . Set up an integral for the volume of the solid obtained by rotating this region about the π‘₯ -axis.

  • A 5 0 πœ‹ ο„Έ 𝑒 π‘₯ 4 0 βˆ’ 4 π‘₯ 2 d
  • B 2 5 πœ‹ ο„Έ 𝑒 π‘₯ 4 0 βˆ’ 2 π‘₯ 4 d
  • C 5 0 πœ‹ ο„Έ 𝑒 π‘₯ 4 0 βˆ’ 2 π‘₯ 4 d
  • D 1 0 πœ‹ ο„Έ 𝑒 π‘₯ 4 0 βˆ’ 2 π‘₯ 2 d
  • E 2 5 πœ‹ ο„Έ 𝑒 π‘₯ 4 0 βˆ’ 4 π‘₯ 2 d

Q2:

Consider the region bounded by the curve 𝑦 = 4 𝑒 βˆ’ 5 π‘₯ 2 and the lines 𝑦 = 0 , π‘₯ = βˆ’ 1 , and π‘₯ = 1 . Set up an integral for the volume of the solid obtained by rotating this region about the π‘₯ -axis.

  • A 3 2 πœ‹ ο„Έ 𝑒 π‘₯ 1 0 βˆ’ 1 0 π‘₯ 2 d
  • B 1 6 πœ‹ ο„Έ 𝑒 π‘₯ 1 0 βˆ’ 5 π‘₯ 4 d
  • C 3 2 πœ‹ ο„Έ 𝑒 π‘₯ 1 0 βˆ’ 5 π‘₯ 4 d
  • D 8 πœ‹ ο„Έ 𝑒 π‘₯ 1 0 βˆ’ 5 π‘₯ 2 d
  • E 1 6 πœ‹ ο„Έ 𝑒 π‘₯ 1 0 βˆ’ 1 0 π‘₯ 2 d

Q3:

Consider the region bounded by the curve 𝑦 = 3 3 π‘₯ c o s 2 and the lines 𝑦 = 0 , π‘₯ = βˆ’ πœ‹ 6 , and π‘₯ = πœ‹ 6 . Set up an integral for the volume of the solid obtained by rotating this region about the π‘₯ -axis.

  • A 1 8 πœ‹ ο„Έ 3 π‘₯ π‘₯ πœ‹ 6 0 4 c o s d
  • B 1 2 πœ‹ ο„Έ 3 π‘₯ π‘₯ πœ‹ 6 0 2 c o s d
  • C 9 πœ‹ ο„Έ 3 π‘₯ π‘₯ πœ‹ 6 0 4 c o s d
  • D 3 πœ‹ ο„Έ 3 π‘₯ π‘₯ πœ‹ 6 0 2 c o s d
  • E 6 πœ‹ ο„Έ 3 π‘₯ π‘₯ πœ‹ 6 0 2 c o s d
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