Explanation Given information: R is the radius of bigger cone and H is the height of the bigger cone. Calculation: Let r denotesradius and h denotes height of the upside-down cone. By similar triangles, the relation obtained is: H − h r = H R h = H ( 1 − r R ) Volume of the upside-down cone: V ( r ) = 1 3 π r 2 h ............. ( i ) = 1 3 π H ( r 2 − r 3 R ) for 0 ≤ r ≤ R . Differentiate V with respect to r , to find the maximum volume of the inverted cone d V d r = 1 3 π H ( 2 r − 3 r 2 R ) Equate d V d r to 0 ⇒ 0 = 1 3 π H ( 2 r − 3 r 2 R ) ⇒ 2 r R = 3 r 2 r = 0 or ⇒ 2 R = 3 r ⇒ r = 2 3 R Differentiating d V d r with respect to r again, d V d r = 1 3 π H ( 2 r

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Chapter 4, Problem 64CRE

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Maximum volume of a right-circular cone placed upside down in a right-circular cone of radius R and height H as shown in given figure.

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Chapter 4, Problem 63CRE

Chapter 4, Problem 65CRE

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Chapter 4 Solutions

Calculus - Standalone book

Ch. 4.1 - Prob. 1PQ Ch. 4.1 - Prob. 2PQ Ch. 4.1 - Prob. 3PQ Ch. 4.1 - Prob. 4PQ Ch. 4.1 - Prob. 1E Ch. 4.1 - Prob. 2E Ch. 4.1 - Prob. 3E Ch. 4.1 - Prob. 4E Ch. 4.1 - Prob. 5E Ch. 4.1 - Prob. 6E

Ch. 4.1 - Prob. 7E Ch. 4.1 - Prob. 8E Ch. 4.1 - Prob. 9E Ch. 4.1 - Prob. 10E Ch. 4.1 - Prob. 11E Ch. 4.1 - Prob. 12E Ch. 4.1 - Prob. 13E Ch. 4.1 - Prob. 14E Ch. 4.1 - Prob. 15E Ch. 4.1 - Prob. 16E Ch. 4.1 - Prob. 17E Ch. 4.1 - Prob. 18E Ch. 4.1 - Prob. 19E Ch. 4.1 - Prob. 20E Ch. 4.1 - Prob. 21E Ch. 4.1 - Prob. 22E Ch. 4.1 - Prob. 23E Ch. 4.1 - Prob. 24E Ch. 4.1 - Prob. 25E Ch. 4.1 - Prob. 26E Ch. 4.1 - Prob. 27E Ch. 4.1 - Prob. 28E Ch. 4.1 - Prob. 29E Ch. 4.1 - Prob. 30E Ch. 4.1 - Prob. 31E Ch. 4.1 - Prob. 32E Ch. 4.1 - Prob. 33E Ch. 4.1 - Prob. 34E Ch. 4.1 - Prob. 35E Ch. 4.1 - Prob. 36E Ch. 4.1 - Prob. 37E Ch. 4.1 - Prob. 38E Ch. 4.1 - Prob. 39E Ch. 4.1 - Prob. 40E Ch. 4.1 - Prob. 41E Ch. 4.1 - Prob. 42E Ch. 4.1 - Prob. 43E Ch. 4.1 - Prob. 44E Ch. 4.1 - Prob. 45E Ch. 4.1 - Prob. 46E Ch. 4.1 - Prob. 47E Ch. 4.1 - Prob. 48E Ch. 4.1 - Prob. 49E Ch. 4.1 - Prob. 50E Ch. 4.1 - Prob. 51E Ch. 4.1 - Prob. 52E Ch. 4.1 - Prob. 53E Ch. 4.1 - Prob. 54E Ch. 4.1 - Prob. 55E Ch. 4.1 - Prob. 56E Ch. 4.1 - 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Maximum volume of a right-circular cone placed upside down in a right-circular cone of radius R and height H as shown in given figure.

Solution Summary: The author calculates the maximum volume of a right-circular cone placed upside down in an upside-down cone of radius R and height H.

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To calculate: Maximum volume of a right-circular cone placed upside down in a right-circular cone of radius R and height H as shown in given figure.

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Chapter 4 Solutions

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Maximum volume of a right-circular cone placed upside down in a right-circular cone of radius R and height H as shown in given figure.