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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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Chapter
Section
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Find a formula for the described function and state its domain.

61. An open rectangular box with volume 2 m3 has a square base. Express the surface area of the box as a function of the length of a side of the base.

To determine

To find: The function of the surface area of the open rectangular box with a square base in terms of the length of a side of the base and the domain of the function.

Explanation

Given:

The volume of the open rectangular box with a square base is 2 m3.

Formula used:

Volume of the rectangular box of length l, width b, height h is, V=l×b×h .

Surface area of the open rectangular box of length l, width b, height h is, S=2(lh+wh)+lb .

Calculation:

Let the length of the open rectangular box be a and the height of the open rectangular box is h.

Since the base of the open rectangular box is a square, the width of the box is same as the length. Therefore, the width of the open rectangular box is a.

Volume of the open rectangular box is, V=a×a×h .

That is, V=a2h

Since the volume of the open rectangular box with a square base is 2 m3, the height of the box is computed as follows:

2=a2hh=2a2

Thus, the surface area of the open rectangular box is S=2(ah+ah)+a2

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