Since the diameter of the cylinder is 10 centimeters and the radius is half of the diameter, the radius is 5 centimeters. The height of the cylinder can be determined from the right triangle formed by the height, the radius, and the axis.
Using the Pythagorean theorem:
(radius)^2 + (height)^2 = (axis)^2
5^2 + (height)^2 = 5^2
25 + (height)^2 = 25
(height)^2 = 0
height = 0
Therefore, the height of the cylinder shown is 0 centimeters.