A cylindrical tin can holding 2 gal.has its height equal to the diameter of its base.Another cylindrical tin can with the same capacity has its height equal to twice the diameter of its base. Find the ratio of the amount of tin required for making the two cans with covers..

Question

A cylindrical tin can holding 2 gal.has its height equal to the diameter of its base.Another cylindrical tin can with the same capacity has its height equal to twice the diameter of its base. Find the ratio of the amount of tin required for making the two cans with covers..
Help me pls..

drwls · Answer

pi*D^2*L is the same for both.
Therefore D1^2*L1 = D2^2*L2
and D1^3 = 2D2^3
Therefore D2/D1 = 1.260

For the areas,
A1 = pi*D1^2/2 + pi*D1*L
= (3/2)pi*D1^2 since D1 = L1

A2 = pi*D2^2/2 + pi*D2*L2
= (5/2)pi*D2^2 since D2 = 2L2
A2/A1 = (5/3)*(D2/D1)^2
= (5/3)*1.5873 = 2.646