well, think about 2d spaces. the geometric representation of the set of numbers 4 units from the x axis (both in the positive and negative directions) would be two lines, would it not? because along the lines y=4 or y=-4, it is constantly 4 units from the x-axis.

extend this to 3d space now...can you start to see the cylinder?

and im not sure about the second question sorry...the notation is kinda throwing me