Question 428043: Find the least amount of material needed to make a square based open box that has a volume of 5000 cubic meters. Answer by htmentor(1343) (Show Source):
You can put this solution on YOUR website! The box is open, so it will have 5 sides.
Let a = the side length of the square bottom
Let h = the height of the box
We are given the volume of the box = 5000.
We need to find a formula for the amount of material required for the box.
The bottom will have area
Each side will have area , and there are 4 of them.
Thus, the total amount of material will be: (1)
The volume of the box,
So
Substitute this value for h into equation (1):
To minimize M, we take the derivative and set = 0:
Solve for a: m
Therefore m
