Finding the Function:[Surface Area of a Box]?

Question

A closed box with a square base has to have a volume of 12,000 cubic inches.

Find a function for the surface area of the box.

A) f (x) = 2x^2 + (72,000 / x)

B) f (x) = 2x^2 + (48,000 / x)

C) f (x) = x^2 + (48,000 / x)

D) f (x) = 2x^2 + (12,000 / x)

Can anyone give me the correct answer and explain the steps?
I want to understand the concept fully for my exam next week.

Thank you in advance.

Answer 1

volume = rx^2 = 12000, r= 12000/x^2

top and bottom square = x^2
left and right square = rx
front and back square = rx

surface area
= 2x^2 + 4rx
= 2x^2 + 4 (12000/x^2) x
= 2x^2 + 48000 / x (b)

Answer 2

So 12000 = x^2*h, hence h= 12000/x^2; thus s=2x^2 + 4x*h = 2x^2 + 4x*12000/x^2 = 2x^2 + 48000/x

Answer 3

LoL, I had problem with this one, long time ago, it is a well known problem but it takes forever because it can't be too high or too low or long or too short, the only way you could do is using variables and replacing it with numbers is error/trial kind of problem.