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A square based prism and a cylinder both have the same height of 4cm^3, based on the concepts of the Cavalieri's principle, what is the approximate circumference of the base of the cylinder?

A square based prism and a cylinder both have the same height of 4cm^3, based on the concepts of the Cavalieri's principle, what is the approximate circumference of the base of the cylinder?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A square based prism and a cylinder both have the same height of 4cm^3, based on the concepts of the Cavalieri's principle, what is the approximate circumference of the base of the cylinder? 

**Multiple Choice** ## Question 3 A square-based prism and a cylinder both have the same height of 4 cm and the same base area. If the volume of the square-based prism is \(452 \, \text{cm}^3\), based on the concepts of Cavalieri's principle, what is the approximate circumference of the base of the cylinder? **Diagrams:** - The diagram shows a cylinder and a square-based prism both having a height of 4 cm. - The height of 4 cm is indicated between the top and bottom surfaces of both the cylinder and prism. **Hint:** 1. Use the volume to find the area of the base. \(V = Bh\) 2. Use the area of the base to find the radius of the circle. \(A = \pi r^2\) 3. Use the radius to find the circumference. \(C = 2\pi r\) **Options:** - A) \(12.8 \, \text{cm}\) - B) \(21.1 \, \text{cm}\) - C) \(35.7 \, \text{cm}\)
Transcribed Image Text:**Multiple Choice** ## Question 3 A square-based prism and a cylinder both have the same height of 4 cm and the same base area. If the volume of the square-based prism is \(452 \, \text{cm}^3\), based on the concepts of Cavalieri's principle, what is the approximate circumference of the base of the cylinder? **Diagrams:** - The diagram shows a cylinder and a square-based prism both having a height of 4 cm. - The height of 4 cm is indicated between the top and bottom surfaces of both the cylinder and prism. **Hint:** 1. Use the volume to find the area of the base. \(V = Bh\) 2. Use the area of the base to find the radius of the circle. \(A = \pi r^2\) 3. Use the radius to find the circumference. \(C = 2\pi r\) **Options:** - A) \(12.8 \, \text{cm}\) - B) \(21.1 \, \text{cm}\) - C) \(35.7 \, \text{cm}\)
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