Buoyancy problem: Deriving an equation for volume of a floating object

Hairy Biped

1. The problem statement, all variables and given/known data
The problem consists of a ball almost completely submerged. The exact question is:
"An object with density ρO and mass m is floating in a pool of fluid with density ρF. Derive an expression for the volume of the object that is above the fluid."

2. Relevant equations
Density of object=mass/volume
Density of fluid= mass fluid/volume fluid

3. The attempt at a solution
I have no idea where to begin.
I know this looks like i'm just fishing for a free answer, but I am not. I tried setting the buoyant force to the (mass of the fluid displaced) * (g) but I don't know how to relate this to the other variables. Any help is greatly appreciated, thanks.

Hairy Biped

would the buoyant force equal the downward force? ie, would Fb=mg?

Redbelly98

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Welcome to Physics Forums

Yes, F_b would have to equal mg if the ball is at rest (i.e. not accelerating). And, as you said, F_b is g times the mass of the displaced fluid.

Hairy Biped

so if bouyant force equals mg, then the mass of the displaced fluid equals the mass of the ball? If so then (density water)(Volume displaced)=(density ball)(volume ball)?