Puzzle of the Week #77 - Bed of Nails

I have a bed of nails where the nails, of equal height, are arranged in a square array with 6cm between adjacent rows and 6cm between adjacent columns. I have a globe, 11cm in diameter, which I place onto the bed of nails. It settles so that it is resting on the tips of four nails.

How much higher will the top of the globe be than the tips of the nails?