Explanation Given information : The initial volume of the block of ice V 0 =1000 cm 3 . The length of block decreasing when melting at the rate 1cm/hr. The rate of decreasing the surface area is to be measured when volume of the block is 27 cm 3 . Formula used : If y is function of variable x such as y ( x ) = f ( x ) = a x n ± b x m then d y d x = a n x n -1 ± b m x m -1 . Calculations: Let a ( t ) be the length of cubical block of ice then its volume is function of time is given by V ( t ) = [ a ( t ) ] 3 and surface area that also function of time is A ( t ) =6 [ a ( t ) ] 2 . The rate of change of area is given by differentiating A ( t ) with respect to t

6th Edition

ISBN: 9781465208880

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

Publisher: Kendall Hunt Publishing

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Chapter 3, Problem 81SP

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To find:The rate ofchange of surface area cubical ice block at given volume.

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Chapter 3, Problem 80SP

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Chapter 3 Solutions

Calculus

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The rate ofchange of surface area cubical ice block at given volume.

Solution Summary: The author calculates the rate of change of surface area cubical ice block at given volume.

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Chapter 3 Solutions