Changing dimensions in a rectangular box Suppose that the

Chapter 3, Problem 22E

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QUESTION:

Problem 22E

Changing dimensions in a rectangular box Suppose that the edge lengths x, y, and z of a closed rectangular box are changing at the following rates:

Find the rates at which the box’s (a) volume, (b) surface area, and (c) diagonal lengthare changing at the instant when x = 4, y = 3, and z = 2.

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QUESTION:

Problem 22E

Changing dimensions in a rectangular box Suppose that the edge lengths x, y, and z of a closed rectangular box are changing at the following rates:

Find the rates at which the box’s (a) volume, (b) surface area, and (c) diagonal lengthare changing at the instant when x = 4, y = 3, and z = 2.

ANSWER:

Solution

Step 1 of 3

In this problem we have to find the changing volume, surface area, and the diagonal length of the closed rectangular box.

Given that

And diagonal length are changing at the instant when x = 4, y = 3, and z = 2.


(a) In this problem shows

 volume

Changing volume is

.’. The changing volume of the box is .


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