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📝 Volumes By Slicing; Disks And Washers

📖 From Calculus • 7. Applications of the Definite Integral In Geometry, Science, and Engineering • 17 questions available

Practice MCQs for Volumes By Slicing; Disks And Washers. 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 solid obtained by rotating the region bounded by \(y=\sqrt{x}\) and \(x=4\) about the \(x\)-axis.

🔹 A. 16π

🔹 B. 8π

🔹 C. 4π

🔹 D. 2π

💡 Difficulty: easy | ✅ Correct: B

Q2. Which integral correctly represents the volume of the solid generated by rotating \(y=\ln(x+1)\) from \(x=0\) to \(x=1\) about the \(x\)-axis?

🔹 A. \( \int_{0}^{1}\pi[\ln(x+1)]^{2}dx \)

🔹 B. \( \pi\int_{0}^{1}[\ln(x+1)]^{2}dx \)

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

🔹 D. \( \pi\int_{0}^{1}\ln(x+1)dx \)

💡 Difficulty: medium | ✅ Correct: B

Q3. Find the volume of the solid generated by rotating the region bounded by \(y=e^{x}\), \(y=0\), \(x=0\), and \(x=1\) about the line \(y=-1\).

🔹 A. \( \pi\big[\tfrac{e^{2}}{2}+2e-\tfrac{5}{2}\big] \)

🔹 B. \( \pi\big[\tfrac{e^{2}}{2}-2e+\tfrac{5}{2}\big] \)

🔹 C. \( \pi\big[\tfrac{e^{2}}{2}+2e+\tfrac{5}{2}\big] \)

🔹 D. \( \pi\big[\tfrac{e^{2}}{2}-2e-\tfrac{5}{2}\big] \)

💡 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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