Buoyancy,volume of air inside barrel

[Kqwert]

Homework Statement

We are using a device(as shown in the image) to blow air into a 200L plastic barrel. We want to know how much air (volume) that is needed to raise the anchor from the seabed.

Homework Equations

The Attempt at a Solution

The anchor will start moving upwards when the sum of forces on it is zero. We have gravitational and buoyant forces. We need to "displace" an unknown amount of water inside the barrel by pumping air into the barrel, corresponding to V,air.

My force balance:
rho, water * g * V,anchor + rho, water*g*V,air - m,anchor*g - m, barrel*g = 0

The solution manual does not include the last term, i.e. m, barrel*g. I guess this is only possible because m, barrel is assumed very small compared to the anchor? Also: Is my reasoning regarding "displacing" an unknown amount of water inside the barrel correct, using Archimede´s principle?

 

[kuruman]

If the mass of the barrel is not given, then you must assume that it is negligible. Your reasoning is correct.