Keep room above the water

An upright sealed rectangular platform has horizontal area 0.20 m², height 0.30 m and unloaded mass 40 kg. It floats in water of density 1000 kg/m³. Dry cargo is carried above the water; orientation remains stable.

What maximum cargo mass leaves at least 0.040 m of freeboard?

Organize the givens & assumptions

A = 0.20 m²
H = 0.30 m
M = 40 kg
ρ = 1000 kg/m³
Minimum freeboard = 0.040 m

Settled hydrostatic equilibrium in uniform gravity; stable stated orientation, no contact forces unless stated, negligible air buoyancy and surface tension, no absorption, trapped gas or spilling.

A $12\ \mathrm{kg}$
B $20\ \mathrm{kg}$
C $52\ \mathrm{kg}$
D $8\ \mathrm{kg}$

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