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a) Determine the ratio of the volume of the sphere to the volume of the cylinder in this situation. b) Determine the ratio of the surface area of the sphere to the surface area of the cylinder in this situation. c) What seems to be true about your answers from parts a) and b)?

a) Determine the ratio of the volume of the sphere to the volume of the cylinder in this situation. b) Determine the ratio of the surface area of the sphere to the surface area of the cylinder in this situation. c) What seems to be true about your answers from parts a) and b)?

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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Archimedes of Syracuse (287-212 BCE) studied many things. One was the relationship between a cylinder and a sphere. In particular, he looked at the situation where the sphere just fits inside the cylinder so that they have the same radius and the height of the cylinder equals the diameter of the sphere. a) Determine the ratio of the volume of the sphere to the volume of the cylinder in this situation. b) Determine the ratio of the surface area of the sphere to the surface area of the cylinder in this situation. c) What seems to be true about your answers from parts a) and b)?
Transcribed Image Text:Archimedes of Syracuse (287-212 BCE) studied many things. One was the relationship between a cylinder and a sphere. In particular, he looked at the situation where the sphere just fits inside the cylinder so that they have the same radius and the height of the cylinder equals the diameter of the sphere. a) Determine the ratio of the volume of the sphere to the volume of the cylinder in this situation. b) Determine the ratio of the surface area of the sphere to the surface area of the cylinder in this situation. c) What seems to be true about your answers from parts a) and b)?
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