Suppose you have a large barrel in the shape of a cylinder of radius 1 meter.  The barrel initially contains water to a depth of 10 cm.  Into the barrel falls a metal cylinder of radius 8 cm and length 1 meter, sinking to the bottom of the barrel.  To what height does the level of the water rise? 

(For the still curious:  You replace the first metal cylinder by a second one which, when dropped into the barrel, is now exactly covered by the water.  How large is this second cylinder?)