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📝 Volumes By Cylindrical Shells

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

Practice MCQs for Volumes By 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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📝 Sample Questions

Q1. When applying the cylindrical‑shell method, which constant factor appears in every integral?

🔹 A. \( \pi \)

🔹 B. \( 2\pi \)

🔹 C. \( \frac{\pi}{2} \)

🔹 D. \( 4\pi \)

💡 Difficulty: easy | ✅ Correct: B

Q2. A water tank is formed by revolving the region bounded by \(y = \sqrt{x}\), \(y = 0\), and \(x = 4\) about the y‑axis. Which integral correctly computes its volume using shells?

🔹 A. \(2\pi\int_{0}^{4} x\sqrt{x}\,dx\)

🔹 B. \(2\pi\int_{0}^{4} \sqrt{x}\,dx\)

🔹 C. \(2\pi\int_{0}^{4} (4-x)\sqrt{x}\,dx\)

🔹 D. \(2\pi\int_{0}^{4} x(4-\sqrt{x})\,dx\)

💡 Difficulty: medium | ✅ Correct: A

Q3. A solid is formed by revolving the region between \(y = e^{x}\) and \(y = 1\) from \(x=0\) to \(x=1\) about the y‑axis. Which integral correctly represents its volume?

🔹 A. \(2\pi\int_{0}^{1} x(e^{x}-1)\,dx\)

🔹 B. \(2\pi\int_{0}^{1} (e^{x}-1)\,dx\)

🔹 C. \(2\pi\int_{0}^{1} x(e^{x}+1)\,dx\)

🔹 D. \(2\pi\int_{0}^{1} (e^{x}+1)\,dx\)

💡 Difficulty: hard | ✅ Correct: A

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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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