Explanation Given: The sides of cube are expanding at a rate of 2 inches per minute. Concept Used: Volume of a cube is: ( side ) 3 Area of base of a cube is: ( side ) 2 Calculation: To determine how fast the volume of the cube is changing the area of the cube’s base is 10 square inches. Find d V d t Where V represents volume of the cube. Since, volume of a cube is V = ( side ) 3 ⇒ d V d t = d d t ( side ) 3 ⇒ d V d t = 3 ( side ) 2 d ( side ) d t ⇒ d V d t = 3 ( side ) 2 d ( side ) d t As, we are given that the sides of cube are expanding at a rate of 2 inches per minute, thus d ( side ) d t

5th Edition

ISBN: 9781429241861

Author: Laura Taalman, Peter Kohn

Publisher: W. H. Freeman

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Chapter 3.5, Problem 42A

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To find how fast the volume of the cube is changing when the area of the cube’s base is 10 square inches.

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Chapter 3.5, Problem 41A

Chapter 3.5, Problem 43A

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Chapter 3 Solutions

Calculus

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To find how fast the volume of the cube is changing when the area of the cube’s base is 10 square inches.

Solution Summary: The author calculates how fast the volume of a cube is changing when the area of its base is 10 square inches.

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To find how fast the volume of the cube is changing when the area of the cube’s base is 10 square inches.

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Chapter 3 Solutions