To Find: The dimension that gives the maximum value for the given data.
The maximum volume that gives the dimension is
Given:
Height of the box
Perimeter
Explanation:
The perimeter of a rectangle whose length and breadth are
A rectangular box with a
Given the height of the box
Perimeter
Find the volume of the rectangular box:
Equate the equation
Thus, the volume of the box is:
Differentiate the above equation:
To find the maximum volume set
So, set
Now, put
Thus, the length and breadth of the rectangular box is:
To find the maximum volume of the rectangle:
Thus, the maximum volume that gives the dimension is
Chapter 4 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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