very quick- surface area of a can?

if you have a tin can and remove the top, the surface area would include the inside of the can right? part one of our problem sheets requires us to calculate the surface area of an opened can, and I can't see why you would discount the surface area of the inside?
so the total surface area of an opened can would be 2(pi)r^2 + 4(pi)(r)(h), right? it seems like an obvious question, but if i ignore the inside of the can i get a much more simple answer than if i include it

It is usual in most types of modelling to say that the thickness of the sheet metal used is negligible, so the surface area is the area of the net of the solid.

(However it could be double in an instance where you may want to cover/paint the can inside and outside)

I see... so in this case, i would take the area as just pi(r^2)+2pi(r)(h)?
seems really odd to me- i would've thought that that the "surface" would basically be anything that gets wet if you submerge it in water- anything not covered/inside, but your answer definitely gives a better answer for my particular question...

As I mentioned
most of the time you must think of it as the amount(area) of sheet metal/card that you will need to "bent into shape" to form the solid, In other words the area of its net.

so
the formula you give is correct.