The density of ice is 917 kg/m3, and the density of sea water is 1025 kg/m3. A swimming polar bear climbs onto a piece of floating ice that has a volume of 3.25 m3. What is the weight of the heaviest bear that the ice can support without sinking completely beneath the water?

Answer 1

When the ice flow is fully submerged,

M*g + V*rho2*g = V*rho1*g

Solve for bear mass, M.
rho2 = ice density = 917 kg/m^3
rho1 = seawater density = 1025 kg/m^3
g cancels out

V = 3.25 m^3

M = 3.25 m^3* 108 kg/m^3 = 351 kg

That mass will sink the ice floe, but not the bear. You need to know the bear's density if you want to include the effect of its own flotation.