A raft measures 1.7m x 0.67m x 0.14m, and it has a mass of 13.5kg. What is the maximum mass that the raft can hold and still stay afloat
Assuming the raft is navigating in fresh water with ρ=1.
Archimedes principle of floatation says that the mass of a floating body equals the mass liquid displaced.
So until the mass exceeds the mass of liquid (fresh water) displaced by the volume of the raft, it will float.
This limit is
V=1.7×0.67×0.14 m³
mass = 1000 kg/m³ * V m³
= 1000V kg
Do not forget to subtract the mass of the raft itself.