You've been given the task of designing a "water couch"-that one could lie on, floating on a lake, for instance-in the form of a flat rectangular slab made of Styrofoam with a density of 85 kg/m 3 . What minimum volume must the slab have so that a 45 kg teenager can lie on top of the slab without getting wet? Optional extra credit (1 point): To explore the bottom of a 15-meter deep lake, your friend Jacques proposes to get a long garden hose, leave one end on land and the other in his mouth for breathing underwater, grab some hand weights and descend to the bottom of the lake to walk around down there. Explain why he will not be able to breathe that way, using a calculation or two (with approximations as needed) to support your argument.