A fish maintains its depth in fresh water by adjusting the air content of porous bone or air sacs to make its average density the same as that of the water. Suppose that with its air sacs collapsed, a fish has a density of 1.05 g/cm3. To what fraction of its expanded body volume must the fish inflate the air sacs to reduce its density to that of water?

V'/V = 1.05

Explanation:

The density is defined with the ratio of the mass to the volume, for the fish with the collapsed sack

ρ₁ = m / V

The density of the fish with the bag full of air is

ρ₂ = m / V'

For the fish to float if it exerts its density must be exactly equal to that of the surrounding water

We clear the mass and match

m = ρ1 V = ρ2 V'

ρ₁ V = ρ₂ V'

V ' / V = ρ₁ / ρ₂

V ' / V = 1.05 / 1

V ' = 1.05 V

This is that the fish should increase its volume by 5%