Calculus - applied optimization problem (open-top box)

A box with a square base and open top is to have a volume of 162,000 cm^3. The material for the bottom costs $3 per square cm while the material for the four sides costs $2 per square cm. Find the dimensions of the least expensive box that can be built.

Thank you in advance!

V = a²*b → b = V/a²

Cost C = 3*a² + 2*4*a*b

C = 3a² + 8V/a

dC/da = 6a + 8V[-1/a²] = 0

6a = 8V/a²

a = 60 cm
b = 45 cm