A cylindrical tin can is to be manufactured so that it will hold a specific volume...

 

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A cylindrical tin can is to be manufactured so that it will hold a specific volume V. If the materials for the ends of the can are twice as expensive as materials for the sides, what shape of can is most economical to manufacture? Find h in terms of r. Let the cost = $c per cm², h is the height of the cylinder and r is the radius of the cylinder. You can assume that the cost is proportional to the surface area since the materials for a tin can have uniform thickness. Ignore the costs of forming the can, which are about the same for cans of any size. A cylindrical tin can is to be manufactured so that it will hold a specific volume V. If the materials for the ends of the can are twice as expensive as materials for the sides, what shape of can is most economical to manufacture? Find h in terms of r. Let the cost = $c per cm², h is the height of the cylinder and r is the radius of the cylinder. You can assume that the cost is proportional to the surface area since the materials for a tin can have uniform thickness. Ignore the costs of forming the can, which are about the same for cans of any size.