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📝 Volumes By Disks And Washers Perpendicular To The Y Axis

📖 From Calculus • 7. Applications of the Definite Integral In Geometry, Science, and Engineering • 20 questions available

Practice MCQs for Volumes By Disks And Washers Perpendicular To The Y Axis. Test your knowledge with carefully crafted questions across easy, medium, and hard difficulty levels.

🔄 Last updated: 2026-07-16

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📝 Sample Questions

Q1. A region is bounded by \(y= \sqrt{x}\), the y‑axis, and \(y=2\). When this region is revolved about the y‑axis, what is the volume of the resulting solid?

🔹 A. \( \displaystyle \pi\int_{0}^{2} (2y)^2\,dy\)

🔹 B. \( \displaystyle \pi\int_{0}^{2} y^2\,dy\)

🔹 C. \( \displaystyle \pi\int_{0}^{2} (y^2+1)^2\,dy\)

🔹 D. \( \displaystyle \pi\int_{0}^{2} (2y+1)^2\,dy\)

💡 Difficulty: easy | ✅ Correct: A

Q2. A solid is generated by rotating the area between \(x= y^{2}\) and \(x=2y\) for \(0\le y\le 1\) about the y‑axis. What is the correct volume integral?

🔹 A. \( \displaystyle \pi\int_{0}^{1}\bigl(2y\bigr)^{2}dy\)

🔹 B. \( \displaystyle \pi\int_{0}^{1}\bigl(y^{2}\bigr)^{2}dy\)

🔹 C. \( \displaystyle \pi\int_{0}^{1}\bigl[(2y)^{2}-(y^{2})^{2}\bigr]dy\)

🔹 D. \( \displaystyle \pi\int_{0}^{1}\bigl[(y^{2})^{2}-(2y)^{2}\bigr]dy\)

💡 Difficulty: medium | ✅ Correct: C

Q3. A cylindrical tank of radius 3 m is filled with water to a height of 4 m. If the water is drained through a hole at the bottom, the work required to lift the water to the top of the tank is equivalent to the volume of a solid generated by rotating which region about the y‑axis?

🔹 A. \( \displaystyle \{(x,y):0\le y\le4,\;0\le x\le3\}\)

🔹 B. \( \{(x,y):0\le y\le3,\;0\le x\le4\}\)

🔹 C. \( \{(x,y):0\le y\le4,\;x=3\}\)

🔹 D. \( \{(x,y):0\le y\le3,\;x=4\}\)

💡 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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