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📝 Volumes By Disks Perpendicular To The X Axis

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

Practice MCQs for Volumes By Disks Perpendicular To The X Axis. 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 \(y=\sqrt{x}\), the x‑axis, and \(x=4\) about the x‑axis.

🔹 A. \(8\pi\)

🔹 B. \(16\pi\)

🔹 C. \(4\pi\)

🔹 D. \(12\pi\)

💡 Difficulty: easy | ✅ Correct: A

Q2. A solid is formed by rotating the region under \(y=\ln(x+1)\) from \(x=0\) to \(x=3\) about the x‑axis. Which integral correctly represents its volume?

🔹 A. \(\displaystyle \pi\int_{0}^{3}\bigl(\ln(x+1)\bigr)^{2}dx\)

🔹 B. \(\displaystyle 2\pi\int_{0}^{3}\ln(x+1)\,dx\)

🔹 C. \(\displaystyle \pi\int_{0}^{3}\ln(x+1)\,dx\)

🔹 D. \(\displaystyle \pi\int_{0}^{3}x\ln(x+1)\,dx\)

💡 Difficulty: medium | ✅ Correct: A

Q3. A solid of revolution is formed by rotating the region bounded by \(y=4-x^{2}\) and the x‑axis from \(x=-2\) to \(x=2\) about the x‑axis. What is the volume?

🔹 A. \( \displaystyle \frac{128\pi}{5}\)

🔹 B. \( \displaystyle \frac{256\pi}{5}\)

🔹 C. \( \displaystyle \frac{64\pi}{5}\)

🔹 D. \( \displaystyle \frac{32\pi}{5}\)

💡 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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