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Concept explainers
26. Constructing an Open Box An open box with a square base is required to have a volume of 10 cubic feet.
(a) Express the amount A of material used to make such a box as a function of the length x of a side of the square base.
(b) How much material is required for a base 1 foot by 1 foot?
(c) How much material is required for a base 2 feet by 2 feet?
(d) Use a graphing utility to graph . For what value of x is A smallest?
![Check Mark](/static/check-mark.png)
To find:
a. To expresses the Amount of material used to make a open box with square base as a function of length of the side of the square base.
Answer to Problem 26AYU
Solution:
a.
Explanation of Solution
Given:
An open box with a square base is required to have a volume to 10 cubic feet.
Calculation:
a. To expresses the Amount of material used to make a open box with square base as a function of length of the side of the square base.
Let represent the side of the square base.
Let represent the height of the box.
Let represent the amount of material required for the box.
The volume of the box , where
Hence height .
Area of the base .
Area of side wall .
![Check Mark](/static/check-mark.png)
To find:
b. To find how much material is required for a base of 1 foot by 1 foot.
Answer to Problem 26AYU
Solution:
b. 41 sq feet
Explanation of Solution
Given:
An open box with a square base is required to have a volume to 10 cubic feet.
Calculation:
b. To find how much material is required for a base of 1 foot by 1 foot.
![Check Mark](/static/check-mark.png)
To find:
c. To find how much material is required for a base of 2 feet by 2 feet.
Answer to Problem 26AYU
Solution:
c. 24 sq feet
Explanation of Solution
Given:
An open box with a square base is required to have a volume to 10 cubic feet.
Calculation:
c. To find how much material is required for a base of 2 feet by 2 feet.
![Check Mark](/static/check-mark.png)
To find:
d. To graph and find value of where is smallest.
Answer to Problem 26AYU
Solution:
d.
Explanation of Solution
Given:
An open box with a square base is required to have a volume to 10 cubic feet.
Calculation:
d. To graph and find value of where is minimum.
From the graph, we can see that the is minimum when .
Chapter 2 Solutions
Precalculus Enhanced with Graphing Utilities
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