Explanation Given: A right circular cylinder of largest volume that can be inscribed in a right circular cone of radius R and altitude H Let radius of cylinder be r and height be h In Δ O A B ∼ Δ E D B by AA similarity O A E D = O B E B R r = H H − h r = R H ( H − h ) Now find the volume of cylinder, V = π r 2 h V ( h ) = π ⋅ R 2 H 2 ( H − h ) 2 h Derivative w.r.t h V ' ( x ) = R 2 π H 2 ( H − h ) 2 − 2 h ( H − h ) R 2 π H 2 For maximum or minimum, V ' ( h ) = 0

6th Edition

ISBN: 9781465208880

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Question

Chapter 4.6, Problem 22PS

To determine

To find: The dimensions of the right circular cylinder.

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Chapter 4.6, Problem 21PS

Chapter 4.6, Problem 23PS

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Chapter 4 Solutions

Calculus

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