Explanation Given: The radius of the sphere is r units. A right circular cylinder is inscribed in a sphere of radius r . Result Used: Pythagorean Theorem: If c denotes the length of the hypotenuse and a and b denote the length of the other two sides of a right angle triangle, then the Pythagorean theorem can be expressed as the Pythagorean equation: a 2 + b 2 = c 2 . Calculation: Let r be the radius of sphere. Let h be the height of the right circular cylinder. Let R be the radius of right circular cylinder. The view of a right circular cylinder inscribed in a sphere of radius is shown below in Figure 1. The volume of the right circular cylinder is, V = π ⋅ R 2 ⋅ h . Since the B E F is a right triangle, by the Pythagoras theorem, R 2 + ( h 2 ) 2 = r 2 R 2 + ( h 2 4 ) = r 2 R 2 = r 2 − h 2 4 Substitute the value of R 2 = r 2 − h 2 4 in V = π R 2 h , V = π ( r 2 − h 2 4 ) h = π ( r 2 h − h 3 4 ) Differentiate V with respect to h , d V d h = π ( r 2 − 3 4 h 2 ) For critical values, d V d h = 0 π ( r 2 "

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ISBN: 9781337772020

Author: Stewart

Publisher: VST

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Chapter 4.5, Problem 23E

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To find: The largest volume of a right circular cylinder which is inscribed in a sphere of radius r.

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Chapter 4.5, Problem 22E

Chapter 4.5, Problem 26E

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Chapter 4 Solutions

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The largest volume of a right circular cylinder which is inscribed in a sphere of radius r.

Solution Summary: The author explains the Pythagorean theorem, where r is the radius of a sphere, h the height of the right circular cylinder, and R is its radius.

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To find: The largest volume of a right circular cylinder which is inscribed in a sphere of radius r.

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Chapter 4 Solutions