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πŸ“ Cylindrical Shells

πŸ“– From Calculus β€’ 7. Applications of the Definite Integral In Geometry, Science, and Engineering β€’ 23 questions available

Practice MCQs for Cylindrical Shells. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

πŸ”„ Last updated: 2026-07-16

7
Easy Questions
10
Medium Questions
6
Hard Questions

πŸ“ Sample Questions

Q1. A region bounded by y = x, the x‑axis, and x = 2 is revolved about the y‑axis. Using the shell method, what is the volume?

πŸ”Ή A. \(8\pi/3\)
πŸ”Ή B. \(16\pi/3\)
πŸ”Ή C. \(32\pi/3\)
πŸ”Ή D. \(4\pi\)

πŸ’‘ Difficulty: easy | βœ… Correct: B

Q2. Find the volume generated by rotating the region between y = √x and y = xΒ² about the line x = –1 using shells. (Choose the correct result.)

πŸ”Ή A. \(29\pi/30\)
πŸ”Ή B. \(Ο€/2\)
πŸ”Ή C. \(Ο€\)
πŸ”Ή D. \(2Ο€\)

πŸ’‘ Difficulty: medium | βœ… Correct: A

Q3. Rotate the region under y = eΛ£ from x = 0 to x = 1 about the y‑axis. What is the exact volume?

πŸ”Ή A. \(2Ο€\)
πŸ”Ή B. \(Ο€e\)
πŸ”Ή C. \(Ο€(e‑1)\)
πŸ”Ή D. \(2Ο€e\)

πŸ’‘ Difficulty: hard | βœ… Correct: A

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πŸ”— Related Topics

πŸ“ Approximating RootsπŸ“ Areas and LimitsπŸ“ Continuity in ApplicationsπŸ“ Continuity of CompositionsπŸ“ Continuity of Inverse Functions
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