Define a metric for an annulus, which makes it seem like the curved wall of a cylinder. 
Can anybody please help me in understanding this question?

Hint: They want you to define a metric in the annulus so that the shortest path between 2 points with the same radius is not the length of the straight line between them, but the length of the shortest arc joining them, as it is if you're forced to walk along the wall of a cylinder. This can then be extended to a metric for points with different radii. 
