Floating Bed Problem: Calculate Volume Under Water

[iamtrojan3]

Homework Statement

There is a large bed floating in sea with the density of 765 kg/m^3. What fraction of the bed's volume will be under the surface of the water? The density of sea water is 1035 kg/m^3.

Homework Equations

Fb = Density * v * gravity

The Attempt at a Solution

I know its a buoyancy problem, but i have no idea where to get started. i can't find the Fb b/c volume's not given. maybe i have to set them equal to each other?
so
765 kg/m^3 * Volume * gravity = 1035 kg/m^3 * V * g
so it woulbd be .739% of the volume.
It seems too easy or is this right?
Thank you!

 

[kuruman]

Call the fraction of the volume that is under water f.

Then the buoyant force is

$$BF = \rho_{water}f V g$$

where V is the entire volume of the bed. Then the weight of the bed in terms of its density and volume is ...

so for the bed to float ...