Unrolling a Cylinder

Peel the label off a can and lay it flat: it is a rectangle. Its height is the can's height, and its width is the distance round the can, the circumference $2\cdot \pi\cdot r$. So the curved side has area $2\cdot \pi\cdot r\cdot h$. Add the two circle ends, $\pi\cdot {r}^{2}$ each.

This cylinder has radius 2 and height 5. The ends make $2\cdot \pi\cdot {2}^{2} = 8\cdot \pi$, the curved side makes $2\cdot \pi\cdot 2\cdot 5 = 20\cdot \pi$, and the total is 28π.

The rule is Surface area of a cylinder: $SA = 2\cdot \pi\cdot {r}^{2}+2\cdot \pi\cdot r\cdot h$. An open pipe would have only the curved part, and a cup only one end: read what the question covers.