1) Volume, V = Area of the base * heigth = (πr^2)*h = 26,000 cm^3
h = 26,000 / (πr^2)
2) Dimesions of the cans
A = Lateral side + base
Lateral side = 2πrh
Base = π(r^2)
A = 2πrh + πr^2
A = 2πr[26,000/πr^2] + π(r^2) = 52,000/r + π(r^2)
3) Optimization
A' =0
A' = -52,000/r^2 + 2πr =0
-52,000 + 2πr^3 = 0
r^3 = 26,000/π
r = ∛[26,000/π]
r = 20.22 cm
h = 26,000 / [π(20.22)^2] = 20.24 cm
