Question

The bottom of a steel "boat" is a 8 m ? 18 m ? 2 cm piece of steel (?_steel = 7900 kg/m³). The sides are made of 1.60 cm thick steel. What minimum height must the sides have for this boat to float in perfectly calm water?
____ cm

Answer 1

2 cm = 2/100 = 0.02 m

thickness of steel = 1.60 cm = 1.60/100 = 0.016 m

Now, for the boat to float in calm water -  

weight = Upthrust

=> weight of the bottom plate+weight of 2 short side plates+weight of 2 long side plates=Upthrust

=> (8x18x0.02x7900x9.8) + (8x0.02xhx2x9.8 x 7900) + (18x0.02xhx2x9.8 x 7900) = Vdg

=> 222969.6 + 24774.4 x h + 55742.4 xh = 8x18xhx1000x9.8

=> 222969.6 + 80516.8 x h = 1411200 x h

=> 222969.6 = 1330683.2 x h

=> h = 0.1676 m = 16.76 cm

So, the minimum height of the boat = 16.76 cm.