Buoyancy to find mass, density and force to submerge

[garrigues]

Homework Statement

A plastic cube, 200mm x 200mm x 200mm, is left in a cylindrical container that has a diameter of 400mm holding sea water, density 1024kg/m^3. The level in the container increases by 30mm as the block floats.
i) Find the mass and density of the cube.
ii) Find the extra downward force needed to completely submerge the cube.

Homework Equations

V(water displaced)
p = m/v

The Attempt at a Solution

i) For the mass, I'm having trouble determining the V(water displaced). Is it 200x200x30mm or the volume of water risen - area of 400mm diameter x 30mm? I leaning towards the former, but then what is the point of mentioning the container diameter?
ii) Probably well wrong here, but is that: pgV(water displaced) - pgV(cube) = extra Force?

 

[voko]

If the water were not displaced, then the cube would just be on its surface. But when water does get displaced, it goes up, so it is contained between the submerged part of the cube and the container walls.

 

[garrigues]

So is it the volume of water risen (Area of 400mm diameter x 30mm) minus 200x200xV(cube submerged)? Problem is, how do I know the V(cube submerged) if I don't have its density?

I'm thinking, calculate V(water displaced) -> calculate mass -> get density.

Thanks voko

 

[voko]

The cylindrical volume at the high water mark is the sum of the original water volume and the submerged part of the cube.