Which are the bst measurements for a 500mL can (cylinder)?

Question

Imagina a can of campbell's which would be its ideal measurements using minimum material?

Answer 1

V = 500 cm^3 = πr²h
A = 2πr(r + h)
h = 500/(πr²)
A = 2π(r² + 500/(πr))
dA/dr = 2π(2r - 500/(πr²)) = 0
2r = 500/(πr²)
r³ = 250/π
r ≈ 4.3 cm
h ≈ 8.6 cm
d ≈ 8.6 cm