Question

Best Dimensions for a Box. A box, open at the top with a square base, is to have a volume of 8000 cubic centimeters. What should the dimensions of the box be if the amount of material used is to be a minimum?

Answer 1

let x be side of square, h is height of box

volume = h*x^2 = 8000
surface area = x^2 + 4xh

get surface area in terms of x, --> h = 8000/x^2
--> SA = x^2 + 32,000/x

take derivative and set equal to 0
--> 2x - 32,000/x^2 = 0
--> 2x^3 = 32,000
--> x = 25.198

Answer 2

I had the volume part correct I just didnt know what to do from there
thank you!!!!!

Answer 3

your welcome