How do you find the dimensions that minimize the amount of cardboard used if a cardboard box without a lid is to have a volume of #8,788 (cm)^3#?
The box will have a square bottom.
Then the amount of cardboard used will be:
For the bottom:
For the sides:
Total area :
The volume of the box=
Substituting that into the formula for the area
To find the minimum, we have to differentiate and set to
The sides will be