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

7th Edition

ISBN: 9781524916817

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

Publisher: Kendall Hunt Publishing

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Differential Equations

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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

Chapter 3, Problem 82SP

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The answer is B, Could you please show the steps to obtain the answer

2. Suppose that U(x, y, z) = x² + y²+ z² represents the temperature of a 3-dimensional solid object at any point (x, y, z). Then F(x, y, z) = -KVU (x, y, z) represents the heat flow at (x, y, z) where K > 0 is called the conductivity constant and the negative sign indicates that the heat moves from higher temperature region into lower temperature region. Answer the following questions. (A) [90%] Compute the inward heat flux (i.e., the inward flux of F) across the surface z = 1 - x² - y². (B) [10%] Use the differential operator(s) to determine if the heat flow is rotational or irrotational.

Could you show why the answer is B Using polar coordinates and the area formula

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

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Chapter 3 Solutions