Archimedes' Principle - Submerged object in a fluid

[somemonkey]

Homework Statement

A 1.25kg wooden block has an iron ball glued to one side. (a) if the blocks floats in water with the iron ball "high and dry," what is the volume of wood that is submerged? (b) If the block is now inverted, so that the iron ball is completely immersed, does the volume of wood that is submerged increase, decrease or remain the same? (c) Calculate the volume of wood that is submerged when the block is in the inverted position.

Homework Equations

Volume submerged = V of solid (density of solid/density of fluid)
Density of water = 1000
Density of iron = 7860
Density of wood = 1220

The Attempt at a Solution

So, for part a, I was thinking that since the iron ball isn't submerged, the amount of water is displaces is equal to its weight.
Therefore, the volume of wood that is submerged can be found with (Vsub/Vsolid) = ((density of wood + density of iron ball)/(density of water)), where (Vsub/Vsolid) is the answer.

For part b and c, I was thinking that the volume of wood will decrease, as when the iron ball is submerged, it displaces a volume of water equal to its own volume.
I know that volume of a sphere is V = (4/3)(pi)(r^3), however I don't know exactly how I would plug it into the equation: (Vsub/Vsolid) = ((density of wood + density of iron ball)/(density of water))

thanks in advance

 

[haruspex]

Density of wood = 1220

Wood that dense is not going to float, with or without an iron ball.

(density of wood + density of iron ball)/(density of water)

It makes no sense to add densities. You can masses and you can add volumes.

(Vsub/Vsolid) is the answer.

Being a ratio of volumes, that will give a dimensionless number, not a volume.

For part b and c, I was thinking that the volume of wood will decrease, as when the iron ball is submerged, it displaces a volume of water equal to its own volume.

Yes.

volume of a sphere is

The shape of the iron mass is irrelevant if you are not given its radius. Unfortunately post #1 does not give its mass either, making it impossible to answer a) and c).