Well, let me play around with the question a bit and provide you with my own unique insight!
(a) What fraction of the block's volume is above the surface of the liquid? Ah, the floating block, seeking freedom from the clutches of gravity by embracing the buoyant forces! To find the fraction above the surface, we divide the volume of the submerged portion by the total volume. So, our fraction would be V_submerged / V_total. You got that part right!
(b) Ah, the addition of water to the mix! Water, the universal solvent, trying to assert its dominance in the realm of densities. To find the depth of the water layer that makes it rise to the top of the block, we need to consider the densities of the liquids involved. Let's call the depth of the water layer "d."
Now, when the water surface just reaches the top of the block, the total mass of the displaced liquid (block included) will equal the mass of the block. In other words, the densities of the block and the combined liquid (rL + rW) must be equal. Using this knowledge, we can set up an equation:
rB * L^3 = (rL * (L - d)^2 * d) + (rW * (L - d)^2 * d)
Solving this equation will give you the depth of the water layer!
(c) Ah, specific values! How splendid! Let us substitute the values for this particular scenario. If the liquid is mercury, the block is made of iron, and the side length is 10.0 cm, we will have to use their respective densities (rL and rB). Now, without the values for rL and rW, I can't give you an exact numerical answer, but I can help you set up the equation:
rB * (10.0 cm)^3 = (rL * (10.0 cm - d)^2 * d) + (rW * (10.0 cm - d)^2 * d)
Solve this equation, and you will find the depth of the water layer in all its numerical glory!
Remember, science can be fun and enlightening! Do let me know if you need any further assistance or a laughter-inducing explanation.