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📝 Variations Of The Method Of Cylindrical Shells

📖 From Calculus • 7. Applications of the Definite Integral In Geometry, Science, and Engineering • 23 questions available

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

🔄 Last updated: 2026-07-16

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Q1. Find the volume of the region bounded by y = x and y = 0 from x = 0 to 2 when rotated about the y‑axis using shells.

🔹 A. \( \frac{16\pi}{3} \)

🔹 B. \( \frac{8\pi}{3} \)

🔹 C. \( 4\pi \)

🔹 D. \( \frac{32\pi}{3} \)

💡 Difficulty: easy | ✅ Correct: A

Q2. A water tank is formed by revolving the upper semicircle \(y=\sqrt{1-x^{2}}\) about the y‑axis. What is its volume?

🔹 A. \( \frac{4\pi}{3} \)

🔹 B. \( \pi \)

🔹 C. \( \frac{2\pi}{3} \)

🔹 D. \( \frac{\pi}{2} \)

💡 Difficulty: medium | ✅ Correct: A

Q3. Find the volume of the solid obtained by rotating the region bounded by y = e^{‑x²}, y = 0, x = 0, x = 1 about the line x = –1 using shells.

🔹 A. \( \pi(1‑e^{‑1}) + \pi\sqrt{\pi}\,\operatorname{erf}(1) \)

🔹 B. \( 2\pi(1‑e^{‑1}) + 2\pi\sqrt{\pi}\,\operatorname{erf}(1) \)

🔹 C. \( \pi(1‑e^{‑1}) \)

🔹 D. \( \pi\sqrt{\pi}\,\operatorname{erf}(1) \)

💡 Difficulty: hard | ✅ Correct: D

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🔗 Related Topics

📝 Approximating Roots 📝 Areas and Limits 📝 Continuity in Applications 📝 Continuity of Compositions 📝 Continuity of Inverse Functions

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