Question 484458
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