1. Given data

• Side of cube: $a = 0.5\,\text{m}$
• Density of water: $\rho_w = 10^3\,\text{kg m}^{-3}$
• Initially, the block floats with $30\%$ of its volume submerged.

2. Volume of the cubical block

$V = a^3 = (0.5)^3 = 0.125\,\text{m}^3$

3. Using floating condition initially

Since the block floats with $30\%$ of its volume submerged,

$V_{\text{sub, initial}} = 0.3V$

The weight of the block equals the buoyant force initially, so the mass of the block is equal to the mass of displaced water:

$m_{\text{block}} = \rho_w(0.3V)$

$m_{\text{block}} = 1000 \times 0.3 \times 0.125 = 37.5\,\text{kg}$

4. Maximum load before full submergence

At the limiting case, the block is just fully submerged. Then the maximum buoyant force corresponds to the full volume of the block submerged.

So maximum supported total mass is:

$m_{\text{total, max}} = \rho_w V = 1000 \times 0.125 = 125\,\text{kg}$

5. Maximum additional mass (weight) that can be put on the block

$m_{\text{load, max}} = m_{\text{total, max}} - m_{\text{block}}$

$m_{\text{load, max}} = 125 - 37.5 = 87.5\,\text{kg}$

6. Option check

• A: $30.1\,\text{kg}$ — incorrect
• B: $87.5\,\text{kg}$ — correct
• C: $65.4\,\text{kg}$ — incorrect
• D: $46.3\,\text{kg}$ — incorrect

Therefore, the correct answer is:

$\boxed{87.5\,\text{kg}}$