SOLUTION: A rectangular box has a square base with edge at least one inch long. It has no top, and the total area of its five sides is 300 in2. What is the maximum possible volume of such a
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Question 843003: A rectangular box has a square base with edge at least one inch long. It has no top, and the total area of its five sides is 300 in2. What is the maximum possible volume of such a box?
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
x = side of base which is square shape
y = height
Total area for five sides without top: .
We will use this solved for y soon: .
V = Volume.
This might also be expressed as
although the previous form allows use of calculus derivative.
Derivative.
.
The maximum occurs for
-
Knowing the x value, find the y value from again, ;
-
Maximum Volume:
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