A flat slab of styrofoam, with a density of 32 kg/m3, floats on a lake. For the steps and strategies involved in solving a similar problem, you may view a Video Tutor Solution. What minimum volume must the slab have so that a 38 kg boy can sit on the slab without it sinking? Express your answer with the appropriate units.

0.0392 m³

Explanation:

Given:

Density of the styrofoam, ρ' = 32 kg/m³

Now, let the volume of the slab = V

the submerged volume be = V;

now, the volume of water displaced will be V

thus,

the buoyant force acting will be = ρVg

where,

ρ is the density of water

g is the acceleration due to gravity

now, the

total downward force acting = weight of the boy + weight of the slab

total downward force acting = 38 * g + ρ' * V * g

for the no sinking condition,

bouyant force should be equal to the total downward force

thus,

ρ * V * g = 38 * g + ρ' * V * g

or

ρ * V = 38 + ρ' * V

on subtituting the values

V (1000 - 32) = 38;

or

V = 0.0392 m³