You can put this solution on YOUR website!
Yes, you are on the right track.
You have surface area as f(x), so to find the min,
differentiate and set to 0.
12x-3000x^-2 = 0
*(1/12)x^2: x^3 - 250 = 0
breath x = 5 cubeRoot(2) cm
L = 15 cubeRoot(2) cm
H = 15/cubeRoot(4) cm
Double check and the product is indeed 1125 cm^3