A 20 cm high polystyrene board with a surface area of 40 dm2 is floating in the water.

Question

a) What fraction of its volume is above the water surface?

b) If a 35 kg child is placed on this board, what will be the fraction of its volume that is above the water surface?

Data: Polystyrene density 300 kg/m3.

Answer 1

Well weight of water displaced = weight of board

Dimensions of board = 0.2 m x 0.4 m²

If x% of volume is under water, weight of water displaced = 0.2 x 0.4 x (x/100) x 1000 x g

(1 m3 of water has mass 1000 kg)

Weight of board = 0.2 x 0.4 x 300 g

These are equal

so (x/100) x 1000 = 300

so x = 30 %

Well the weight of the board etc increases by 35g

So 0.2 x 0.4 x 300g + 35g = 0.2 x 0.4 x (x/100) x 1000 x g

So 24 + 35 = 0.8 x

So x = 73.75