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📝 Volumes By Washers Perpendicular To The X Axis

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

Practice MCQs for Volumes By Washers 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. A solid is formed by rotating the region bounded by \(y=x^2\) and \(y=4\) about the x‑axis. What is the volume?

🔹 A. \( \displaystyle \pi\int_{-2}^{2}(4-x^2)^2dx \)

🔹 B. \( \displaystyle \pi\int_{-2}^{2}(4^2 - x^4)dx \)

🔹 C. \( \displaystyle \pi\int_{-2}^{2}(4+x^2)^2dx \)

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

💡 Difficulty: easy | ✅ Correct: A

Q2. A region bounded by \(y= \ln x\), \(y=0\), \(x=1\), and \(x=e\) is revolved about the x‑axis. Which integral gives the volume?

🔹 A. \( \displaystyle \pi\int_{1}^{e}(\ln x)^2dx \)

🔹 B. \( \displaystyle \pi\int_{1}^{e}(\ln x)dx \)

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

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

💡 Difficulty: medium | ✅ Correct: A

Q3. A solid is formed by rotating the region between \(y = x^2\) and \(y = 2x\) from \(x=0\) to \(x=2\) about the x‑axis. What is the exact volume?

🔹 A. \( \displaystyle \frac{56\pi}{15} \)

🔹 B. \( \displaystyle \frac{64\pi}{15} \)

🔹 C. \( \displaystyle \frac{48\pi}{15} \)

🔹 D. \( \displaystyle \frac{72\pi}{15} \)

💡 Difficulty: hard | ✅ Correct: B

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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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