Look at the attached diagram.
The base of this cone would be a circle touching all of the edges of the cube's base. You can see that the diameter of the base is going to be 10 cm, and that the radius would then be 5.
As for the height, it would be at its largest going from top to bottom in that cube, which is 10 cm.
r = 5 cm
d = 10 cm
h = 10 cm
