📝 Theorem Of Pappus

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

Practice MCQs for Theorem Of Pappus. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-16

Easy Questions

Medium Questions

Hard Questions

Q1. What does Pappus's first centroid theorem state about the volume of a solid of revolution?

🔹 A. The volume equals the product of the area of the generating region and the distance traveled by its centroid.

🔹 B. The volume equals the surface area of the generating region times the radius of rotation.

🔹 C. The volume equals the area of the generating region divided by the distance traveled by its centroid.

🔹 D. The volume equals the length of the generating curve times the circumference of the rotation.

💡 Difficulty: easy | ✅ Correct: A

Q2. A torus is formed by rotating a circle of radius \(r=2\) about an axis \(5\) units from its center. What is the volume of the torus?

🔹 A. \(40\pi^2\)

🔹 B. \(16\pi^2\)

🔹 C. \(32\pi\)

🔹 D. \(64\pi\)

💡 Difficulty: medium | ✅ Correct: D

Q3. Derive Pappus's second theorem by integrating the surface area of a surface of revolution. Which integral expression leads to the theorem?

🔹 A. \(\displaystyle SA = \int 2\pi y\,ds\)

🔹 B. \(\displaystyle SA = \int \pi y^{2}\,dx\)

🔹 C. \(\displaystyle SA = \int y\,dx\)

🔹 D. \(\displaystyle SA = \int 2\pi x\,dy\)

💡 Difficulty: hard | ✅ Correct: A

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