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📝 Other Axes Of Revolution

📖 From Calculus • 7. Applications of the Definite Integral In Geometry, Science, and Engineering • 18 questions available

Practice MCQs for Other Axes Of Revolution. 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 region is bounded by \(y=x^2\) and \(y=4\). Find the volume of the solid obtained by rotating this region about the horizontal line \(y=5\).

🔹 A. \(V=\pi\int_{-2}^{2}(5- x^2)^2dx\)

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

🔹 C. \(V=2\pi\int_{-2}^{2}(5- x^2)dx\)

🔹 D. \(V=\pi\int_{-2}^{2}(5-4)^2dx\)

💡 Difficulty: easy | ✅ Correct: A

Q2. A water tank is formed by rotating the region between \(y=x^3\) and \(y=8\) on \([0,2]\) about the line \(x=2\). What is the correct washer integral for its volume?

🔹 A. \(V=\pi\int_{0}^{2}\big[(8-2)^2-(x^3-2)^2\big]dx\)

🔹 B. \(V=\pi\int_{0}^{2}\big[(2-8)^2-(2-x^3)^2\big]dx\)

🔹 C. \(V=\pi\int_{0}^{2}\big[(2-8)^2-(2-x^3)^2\big]dx\)

🔹 D. \(V=\pi\int_{0}^{2}\big[(8-2)^2-(2-x^3)^2\big]dx\)

💡 Difficulty: medium | ✅ Correct: D

Q3. A region bounded by \(y=\sqrt{x}\) and \(y=\frac{x}{2}\) from \(x=0\) to \(x=4\) is revolved about the line \(y=6\). Which integral correctly computes the volume using washers?

🔹 A. \(V=\pi\int_{0}^{4}\big[(6-\tfrac{x}{2})^{2}-(6-\sqrt{x})^{2}\big]dx\)

🔹 B. \(V=\pi\int_{0}^{4}\big[(6-\sqrt{x})^{2}-(6-\tfrac{x}{2})^{2}\big]dx\)

🔹 C. \(V=2\pi\int_{0}^{4}(6-\sqrt{x})(6-\tfrac{x}{2})dx\)

🔹 D. \(V=\pi\int_{0}^{4}(6^{2})dx\)

💡 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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