Design a cylindrical can (with a lid) to contain 5 liters (= 5000 cm3) of water, using the minimum amount of metal.

Question

diameter___?___cm

height______?__cm

Answer 1

V = πr²h = 5000

Surface area = 2πrh + 2πr²

h = 5000/πr²

SA = 2πr(5000/πr²) + 2πr²= 10000/r + 2πr²

SA’ = -10000/r² + 4πr = 0

10000/r² = 4πr

r³ = 2500/π

r = 9.267 cm

d = 18.533 cm

h = 5000/π(9.267)²= 18.533 cm