A cubical block of side 0.5m floats on water with 30% of its volume submerged.

Let the side of the cubical block be L = 0.5 m.
The volume of the block is V = L³ = (0.5 m)³ = 0.125 m³.
The block floats on water with 30% of its volume submerged. Therefore, the submerged volume is V_s = 0.30 * V = 0.30 * 0.125 m³ = 0.0375 m³.
The density of water is ρ = 1000 kg/m³.
The mass of the water displaced is equal to the mass of the block (Archimedes' principle).
Mass of water displaced = ρ * V_s = 1000 kg/m³ * 0.0375 m³ = 37.5 kg.
However, this is only 30% of the volume. To find the mass of the block, we can use the fact that the buoyant force (equal to the weight of the displaced water) is equal to the weight of the block.
Let's assume that '30?' in the question refers to 30% of the block's volume being submerged.
Then the submerged height is h = 0.3 * 0.5m = 0.15m
The submerged volume is V_s = L²h = (0.5m)² * (0.15m) = 0.0375 m³
The mass of the displaced water is M_w = ρV_s = 1000 kg/m³ * 0.0375 m³ = 37.5 kg
Since the block is floating, the mass of the block (M) is equal to the mass of the water displaced:
M = 37.5 kg
This is not one of the options. Let's reconsider the question and solution. It seems there's an error in either the question or the provided solution.
Let's assume the solution intended to calculate the mass using the submerged volume:
M = ρV_s = 1000 kg/m³ * 0.3 * 0.125 m³ = 37.5 kg. This is not among the options.
Let's try a different approach. Let the height of the submerged portion be h. Then the submerged volume is (0.5)²h = 0.25h.
The buoyant force is equal to the weight of the block: ρ_water * g * (0.25h) = M * g, where M is the mass of the block. The volume of the block is 0.125 m³.
Let the density of the block be ρ_block. Then M = ρ_block * 0.125 m³
The submerged volume is 0.3 * 0.125 m³ = 0.0375 m³
The mass of the block is equal to the mass of the water displaced: M = ρ_water * V_submerged = 1000 kg/m³ * 0.0375 m³ = 37.5 kg. This is still not among the options.
There appears to be an inconsistency between the question and the given solution. The provided solution appears to have errors and does not accurately reflect the given problem statement or options.