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Concept explainers
To find:
a. To expresses the Volume of a box as a function of length of the side of the square cut from each corner of a square cardboard.
![Check Mark](/static/check-mark.png)
Answer to Problem 25AYU
Solution:
a.
Explanation of Solution
Given:
“An open box with a square base is made from a square piece of cardboard of 24” on a side by cutting out a square from each corner and folding the sides.
Calculation:
a. To expresses the Volume of a box as a function of length of the side of the square cut from each corner of a square cardboard.
The following figure describes the problem:
Let represent the side of the square that is cut from each corner of the cardboard.
Let represent the side of the box.
Let represent the height of the box.
The volume of the box .
From the figure, and .
Hence, the volume .
To find:
b. To find volume , if a 3 inch square is cut out.
![Check Mark](/static/check-mark.png)
Answer to Problem 25AYU
Solution:
b. 972 cubic inches
Explanation of Solution
Given:
“An open box with a square base is made from a square piece of cardboard of 24” on a side by cutting out a square from each corner and folding the sides.
Calculation:
b. To find volume , if a 3 inch square is cut out .
To find:
c. To find volume , if a 10 inch square is cut out.
![Check Mark](/static/check-mark.png)
Answer to Problem 25AYU
Solution:
c. 160 cubic inches
Explanation of Solution
Given:
“An open box with a square base is made from a square piece of cardboard of 24” on a side by cutting out a square from each corner and folding the sides.
Calculation:
c. To find volume , if a 10 inch square is cut out .
To find:
d. To graph and find value of where is largest.
![Check Mark](/static/check-mark.png)
Answer to Problem 25AYU
Solution:
d.
Explanation of Solution
Given:
“An open box with a square base is made from a square piece of cardboard of 24” on a side by cutting out a square from each corner and folding the sides.
Calculation:
d. To graph and find value of where is largest.
From the graph, we can see that the volume is maximum (1024 cubic inch) when .
Chapter 2 Solutions
Precalculus Enhanced with Graphing Utilities
Additional Math Textbook Solutions
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus & Its Applications (14th Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
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