A box with a square base and open top must have a volume of 32000 cm3. Find the dimensions of the box that minimize the amount of material used. 1 cm (length and width) 2 cm (height)
A box with a square base and open top must have a volume of 32000 cm3. Find the dimensions of the box that minimize the amount of material used. 1 cm (length and width) 2 cm (height)
Thanks!
Let s = the side of the base
Let h = the height of the box
The area of the base is
The area of the 4 sides is
You want to minimize
The volume must be 32000 so
Find the derivative of M, set it equal to 0 and solve for s. Then solve for h.