Optimizing a Fish's Swim Bladder for Suspension in Seawater

[kbyws37]

A fish uses a swim bladder to change its density so it is equal to that of water, enabling it to remain suspended under water. If a fish has an average density of 1080 kg/m^3 and mass 16.1 g with the bladder completely deflated, to what volume must the fish inflate the swim bladder in order to remain suspended in seawater of density 1050 kg/m^3?

I am not really sure how to start this problem. And I am not sure what to do with the mass they have given me.

 

[OlderDan]

Assume the volume of the swim bladder is added to the normal volume of the fish with the bladder deflated. No other part of the fish is compressed as the bladder fills. What happens to the density of an object if you change its volume without changing mass? What must the density of an object be (compared to the density of the fluid) for it to be neutrally buoyant?

 

[rfb13]

One Approach

Seems like it just a matter of ratios. The percent change in volume of the fish should be the same at the percent change in density. Vb = Vf – Vi, where Vb is the volume of the bladder, Vf is the final volume of the fish and Vi is the initial volume of the fish. Vi is essentially given as 16.1g / 1080 kg/m3. The final volume of the fish, Vf = Vi(1080 / 1050). Plug it all in and Bob’s your Uncle.

Randy