cylindrical can w/ height H, radius r

[New2Math]

Can anyone make sense of this question? I am having trouble, understanding how it should look, should it be graphed?

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.

 

[Dr.Peterson]

Can anyone make sense of this question? I am having trouble, understanding how it should look, should it be graphed?

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.

What is it that you don't understand?

It will look like any ordinary cylindrical can, with circular ends. You have to find the radius and height that will minimize the cost for a given volume.

The only problem is that the description is inconsistent. First it says that the materials for the ends cost more (per cm², presumably), but then it gives one cost per cm² (for the whole can), and says the cost is proportional to the surface area. (The cost c is irrelevant to anything you are asked to do, as there is no other mention of specific costs.) It also says the volume is given, which should yield specific values for h and r, but then says to find h in terms of r (e.g. a ratio) as if they were asking for the shape without having specified the volume.

Where did this come from? Did you quote it exactly?

 

[hieutrungpro]

Can anyone make sense of this question? I am having trouble, understanding how it sho

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.

 

[Dr.Peterson]

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.

There is no value in just repeating the problem with no additional information. Can you answer my questions, clarifying what parts you don't understand? And can you confirm that it is properly copied, from a source that we can expect to make sense?

 

[JeffM]

Can anyone make sense of this question? I am having trouble, understanding how it should look, should it be graphed?

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.

Please read https://www.freemathhelp.com/forum/threads/112086-Guidelines-Summary?p=436773#post436773

The obvious way to attack this problem, which is very badly worded, is through differential calculus. Have you studied that?

To minimize cost, you will need a cost function. That cost function will be a sum of functions, one for the two end pieces and one for the side piece. Those functions will require creating expressions for the surface area of of the sides of the can and the ends of the can, for a can of volume V.

Start by getting the two expressions for surface area. What do you get?