Volume of opened objects?

[JulianMathHelp]

I know that for 3d objects that are closed off on all ends, and hollow, the volume is counting the hollow space as the object is occupying the space, but what about 3d objects that are missing a face? For example, a cube that is missing a face? Would you still count the open area with the volume?

My understanding would be that you would still do, as the object still is occupying that amount of space.

 

[lev888]

I know that for 3d objects that are closed off on all ends, and hollow, the volume is counting the hollow space as the object is occupying the space, but what about 3d objects that are missing a face? For example, a cube that is missing a face? Would you still count the open area with the volume?

My understanding would be that you would still do, as the object still is occupying that amount of space.

Can you post the problem where such shape is used?

 

[Dr.Peterson]

As I understand it, the "volume" of a can, whether opened or closed, is the amount of metal it is made of. This is why we have the separate word "capacity" to refer to the volume of the contents. But it is at least debatable that the volume of a closed can could be taken as you do.

I would expect anyone writing a question about such an object to carefully specify what is intended. I don't think I've ever seen a question (in the abstract, and not referring to a physical object) about the volume of a cube missing a face. That isn't really a mathematical concept. (And the surface area, too, would be questionable, as you might want to count both sides of each surface (e.g., in a real-life problem, this would relate to the amount of paint needed to coat all exposed surfaces).

I, too, want to see an example of an actual problem of the sort you are asking about. I think you are thinking too hard about hypothetical questions that just aren't asked.