A box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the box that minimize the amount of material used.

Question

anonymous · Answer

V = 4,000 = x^2 (h), where x is the one side of the base, h is the height and V is the volume 
S = x^2 + 4(x)(h), where S is the surface area. 
h = 4,000/(x^2) 
S = x^2 + 16,000(1/x) 
differentiate S with respect to x 
dS/dx = 2x - 16,000/x^2 = 0 since dS/dx = 0 is a minimum 
2x^3 - 16,000 = 0 
x^3 = 8,000, x = 20 
The sides are 20 cm, and the height is 10 cm

anonymous · Answer

Does that help?

anonymous · Answer

why did you set the derivative of S = 0

anonymous · Answer

idk yahoo lol

anonymous · Answer

hahaha. well thanks anyway lol. the answer came up as correct. I'll try and figure out what was done lol

anonymous · Answer

lol no problem , good luck with the rest.

anonymous · Answer

thank you!

anonymous · Answer

your welcome!