Explanation Given information: A rectangular box B with minimum surface area and fixed volume V . Formula used: The volume of the rectangular box is l b h . Calculation: Total surface area of the open box is: S = l b + 2 ( b h + h l ) = l b + 2 h ( b + l ) ...... (1) Find the value of h , from the volume of the rectangular box. V = l b h h = V l b Also, rewrite as l b = V h Substitute the above values in equation (1). S = V h + 2 h ( b + l ) Find the derivative of S with respect to h . d S d h = − V h 2 + 2 ( b + l ) For the minimum surface area, derivative will be 0 To determine (b) Find the dimensions of B .

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

4th Edition

ISBN: 9781319312886

Author: Rogawski, Jon, Adams, Colin, FRANZOSA, Robert

Publisher: W. H. Freeman

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Question

Chapter 14.7, Problem 55E

To determine

(a)

Check the box B is a cube. If not, write how its differ from a cube.

To determine

(b)

Find the dimensions of B.

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Chapter 14.7, Problem 54E

Chapter 14.7, Problem 56E

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Chapter 14 Solutions

Loose-Leaf Version for Calculus: Early Transcendentals Single Variable

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E

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(a) Check the box B is a cube. If not, write how its differ from a cube.

Solution Summary: The author explains that the box B is not a cube.