Explanation Given: The surface area of the portion of the sphere of radius R between two horizontal planes z = a and z = b is equal to the surface area of the corresponding portion of the circumscribed cylinder. Calculation: Surface area of the sphere = ∫ ϕ = 0 2 π ∫ θ = sin − 1 ( a R ) θ = sin − 1 ( b R ) ( R cos θ ) d ϕ R d θ = R 2 ∫ ϕ = 0 2 π d ϕ ∫ θ = sin − 1 ( a R )

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 17.4, Problem 41E

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The proof for results of Archimedes

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Chapter 17.4, Problem 40E

Chapter 17.4, Problem 42E

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Chapter 17 Solutions

CALCULUS (CLOTH)

Ch. 17.1 - Prob. 1PQ Ch. 17.1 - Prob. 2PQ Ch. 17.1 - Prob. 3PQ Ch. 17.1 - Prob. 4PQ Ch. 17.1 - Prob. 1E Ch. 17.1 - Prob. 2E Ch. 17.1 - Prob. 3E Ch. 17.1 - Prob. 4E Ch. 17.1 - Prob. 5E Ch. 17.1 - Prob. 6E

Ch. 17.1 - Prob. 7E Ch. 17.1 - Prob. 8E Ch. 17.1 - Prob. 9E Ch. 17.1 - Prob. 10E Ch. 17.1 - Prob. 11E Ch. 17.1 - Prob. 12E Ch. 17.1 - Prob. 13E Ch. 17.1 - Prob. 14E Ch. 17.1 - Prob. 15E Ch. 17.1 - Prob. 16E Ch. 17.1 - Prob. 17E Ch. 17.1 - Prob. 18E Ch. 17.1 - Prob. 19E Ch. 17.1 - Prob. 20E Ch. 17.1 - Prob. 21E Ch. 17.1 - Prob. 22E Ch. 17.1 - Prob. 23E Ch. 17.1 - Prob. 24E Ch. 17.1 - Prob. 25E Ch. 17.1 - Prob. 26E Ch. 17.1 - Prob. 27E Ch. 17.1 - Prob. 28E Ch. 17.1 - Prob. 29E Ch. 17.1 - Prob. 30E Ch. 17.1 - Prob. 31E Ch. 17.1 - Prob. 32E Ch. 17.1 - Prob. 33E Ch. 17.1 - Prob. 34E Ch. 17.1 - Prob. 35E Ch. 17.1 - Prob. 36E Ch. 17.1 - Prob. 37E Ch. 17.1 - Prob. 38E Ch. 17.1 - Prob. 39E Ch. 17.1 - Prob. 40E Ch. 17.1 - Prob. 41E Ch. 17.1 - Prob. 42E Ch. 17.1 - Prob. 43E Ch. 17.1 - Prob. 44E Ch. 17.1 - Prob. 45E Ch. 17.1 - Prob. 46E Ch. 17.1 - Prob. 47E Ch. 17.1 - Prob. 48E Ch. 17.1 - Prob. 49E Ch. 17.1 - Prob. 50E Ch. 17.1 - Prob. 51E Ch. 17.1 - Prob. 52E Ch. 17.1 - Prob. 53E Ch. 17.1 - Prob. 54E Ch. 17.1 - Prob. 55E Ch. 17.1 - Prob. 56E Ch. 17.1 - Prob. 57E Ch. 17.2 - Prob. 1PQ Ch. 17.2 - Prob. 2PQ Ch. 17.2 - Prob. 3PQ Ch. 17.2 - Prob. 4PQ Ch. 17.2 - Prob. 1E Ch. 17.2 - Prob. 2E Ch. 17.2 - Prob. 3E Ch. 17.2 - Prob. 4E Ch. 17.2 - Prob. 5E Ch. 17.2 - Prob. 6E Ch. 17.2 - Prob. 7E Ch. 17.2 - Prob. 8E Ch. 17.2 - Prob. 9E Ch. 17.2 - Prob. 10E Ch. 17.2 - Prob. 11E Ch. 17.2 - Prob. 12E Ch. 17.2 - Prob. 13E Ch. 17.2 - Prob. 14E Ch. 17.2 - Prob. 15E Ch. 17.2 - Prob. 16E Ch. 17.2 - Prob. 17E Ch. 17.2 - Prob. 18E Ch. 17.2 - Prob. 19E Ch. 17.2 - Prob. 20E Ch. 17.2 - Prob. 21E Ch. 17.2 - Prob. 22E Ch. 17.2 - Prob. 23E Ch. 17.2 - Prob. 24E Ch. 17.2 - Prob. 25E Ch. 17.2 - Prob. 26E Ch. 17.2 - Prob. 27E Ch. 17.2 - Prob. 28E Ch. 17.2 - Prob. 29E Ch. 17.2 - Prob. 30E Ch. 17.2 - Prob. 31E Ch. 17.2 - Prob. 32E Ch. 17.2 - Prob. 33E Ch. 17.2 - Prob. 34E Ch. 17.2 - Prob. 35E Ch. 17.2 - Prob. 36E Ch. 17.2 - Prob. 37E Ch. 17.2 - Prob. 38E Ch. 17.2 - Prob. 39E Ch. 17.2 - Prob. 40E Ch. 17.2 - Prob. 41E Ch. 17.2 - Prob. 42E Ch. 17.2 - Prob. 43E Ch. 17.2 - Prob. 44E Ch. 17.2 - Prob. 45E Ch. 17.2 - Prob. 46E Ch. 17.2 - Prob. 47E Ch. 17.2 - Prob. 48E Ch. 17.2 - Prob. 49E Ch. 17.2 - Prob. 50E Ch. 17.2 - Prob. 51E Ch. 17.2 - Prob. 52E Ch. 17.2 - Prob. 53E Ch. 17.2 - Prob. 54E Ch. 17.2 - Prob. 55E Ch. 17.2 - Prob. 56E Ch. 17.2 - Prob. 57E Ch. 17.2 - Prob. 58E Ch. 17.2 - Prob. 59E Ch. 17.2 - Prob. 60E Ch. 17.2 - Prob. 61E Ch. 17.2 - Prob. 62E Ch. 17.2 - Prob. 63E Ch. 17.2 - Prob. 64E Ch. 17.2 - Prob. 65E Ch. 17.2 - Prob. 66E Ch. 17.2 - Prob. 67E Ch. 17.2 - Prob. 68E Ch. 17.2 - Prob. 69E Ch. 17.2 - Prob. 70E Ch. 17.2 - Prob. 71E Ch. 17.2 - Prob. 72E Ch. 17.2 - Prob. 73E Ch. 17.2 - Prob. 74E Ch. 17.2 - Prob. 75E Ch. 17.3 - Prob. 1PQ Ch. 17.3 - Prob. 2PQ Ch. 17.3 - Prob. 3PQ Ch. 17.3 - Prob. 4PQ Ch. 17.3 - Prob. 1E Ch. 17.3 - Prob. 2E Ch. 17.3 - Prob. 3E Ch. 17.3 - Prob. 4E Ch. 17.3 - Prob. 5E Ch. 17.3 - Prob. 6E Ch. 17.3 - Prob. 7E Ch. 17.3 - Prob. 8E Ch. 17.3 - Prob. 9E Ch. 17.3 - Prob. 10E Ch. 17.3 - Prob. 11E Ch. 17.3 - Prob. 12E Ch. 17.3 - Prob. 13E Ch. 17.3 - Prob. 14E Ch. 17.3 - Prob. 15E Ch. 17.3 - Prob. 16E Ch. 17.3 - Prob. 17E Ch. 17.3 - Prob. 18E Ch. 17.3 - Prob. 19E Ch. 17.3 - Prob. 20E Ch. 17.3 - Prob. 21E Ch. 17.3 - Prob. 22E Ch. 17.3 - Prob. 23E Ch. 17.3 - Prob. 24E Ch. 17.3 - Prob. 25E Ch. 17.3 - Prob. 26E Ch. 17.3 - Prob. 27E Ch. 17.3 - Prob. 28E Ch. 17.3 - Prob. 29E Ch. 17.3 - Prob. 30E Ch. 17.3 - Prob. 31E Ch. 17.3 - Prob. 32E Ch. 17.3 - Prob. 33E Ch. 17.3 - Prob. 34E Ch. 17.3 - Prob. 35E Ch. 17.4 - Prob. 1PQ Ch. 17.4 - Prob. 2PQ Ch. 17.4 - Prob. 3PQ Ch. 17.4 - Prob. 4PQ Ch. 17.4 - Prob. 5PQ Ch. 17.4 - Prob. 6PQ Ch. 17.4 - Prob. 1E Ch. 17.4 - Prob. 2E Ch. 17.4 - Prob. 3E Ch. 17.4 - Prob. 4E Ch. 17.4 - Prob. 5E Ch. 17.4 - Prob. 6E Ch. 17.4 - Prob. 7E Ch. 17.4 - Prob. 8E Ch. 17.4 - Prob. 9E Ch. 17.4 - Prob. 10E Ch. 17.4 - Prob. 11E Ch. 17.4 - Prob. 12E Ch. 17.4 - Prob. 13E Ch. 17.4 - Prob. 14E Ch. 17.4 - Prob. 15E Ch. 17.4 - Prob. 16E Ch. 17.4 - Prob. 17E Ch. 17.4 - Prob. 18E Ch. 17.4 - Prob. 19E Ch. 17.4 - Prob. 20E Ch. 17.4 - 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Prob. 12E Ch. 17.5 - Prob. 13E Ch. 17.5 - Prob. 14E Ch. 17.5 - Prob. 15E Ch. 17.5 - Prob. 16E Ch. 17.5 - Prob. 17E Ch. 17.5 - Prob. 18E Ch. 17.5 - Prob. 19E Ch. 17.5 - Prob. 20E Ch. 17.5 - Prob. 21E Ch. 17.5 - Prob. 22E Ch. 17.5 - Prob. 23E Ch. 17.5 - Prob. 24E Ch. 17.5 - Prob. 25E Ch. 17.5 - Prob. 26E Ch. 17.5 - Prob. 27E Ch. 17.5 - Prob. 28E Ch. 17.5 - Prob. 29E Ch. 17.5 - Prob. 30E Ch. 17.5 - Prob. 31E Ch. 17.5 - Prob. 32E Ch. 17.5 - Prob. 33E Ch. 17.5 - Prob. 34E Ch. 17.5 - Prob. 35E Ch. 17.5 - Prob. 36E Ch. 17.5 - Prob. 37E Ch. 17.5 - Prob. 38E Ch. 17 - Prob. 1CRE Ch. 17 - Prob. 2CRE Ch. 17 - Prob. 3CRE Ch. 17 - Prob. 4CRE Ch. 17 - Prob. 5CRE Ch. 17 - Prob. 6CRE Ch. 17 - Prob. 7CRE Ch. 17 - Prob. 8CRE Ch. 17 - Prob. 9CRE Ch. 17 - Prob. 10CRE Ch. 17 - Prob. 11CRE Ch. 17 - Prob. 12CRE Ch. 17 - Prob. 13CRE Ch. 17 - Prob. 14CRE Ch. 17 - Prob. 15CRE Ch. 17 - Prob. 16CRE Ch. 17 - Prob. 17CRE Ch. 17 - Prob. 18CRE Ch. 17 - Prob. 19CRE Ch. 17 - Prob. 20CRE Ch. 17 - Prob. 21CRE Ch. 17 - Prob. 22CRE Ch. 17 - 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The proof for results of Archimedes

Solution Summary: The author analyzes how the surface area of the sphere of radius R between two horizontal planes z = a and b is equal to the circumscribed cylinder surface.

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The proof for results of Archimedes

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Chapter 17 Solutions