1. The problem statement, all variables and given/known data A hollow sphere of inner radius 9.0 cm and outer radius 10.0 cm floats half submerged in a liquid of specific gravity 0.80. (a) Calculate the density of the material of which the sphere is made. (b) What would be the density of a liquid in which the hollow sphere would just float completely submerged? Density of liquid = 800 kg/m^3 Outer radius = 0.10 m ; inner radius = 0.09 m 2. Relevant equations 3. The attempt at a solution Because it's half submerged so the volume would be: V = (0.5) (4 pi / 3) * (outer radius^3 ) = 2.09 x 10^-3 m^3 The force on an object is equal to the weight of displaced fluid. If the sphere is half-submerged, we can find the displaced volume of fluid and then its weight. so ρgV = mg which implies that ρV = m therefore mass of the sphere = (800 kg/m^3)(2.09 x 10^-3 m^3)= 1.68 kg Then V of the sphere, actually the volume of the mass in the sphere so now we take (4 pi / 3) * (outer radius^3- inner radius^3 ) = (4 pi / 3) * (0.1^3 )-(0.09)^3) = 1.135 x 10^-3 m^3 ρ= 1.68 kg / 1.135 x 10^-3 m^3 = 1479 kg/m^3 ? This is what I worked out but I'm a little unsure regarding the volumes I've taken? For part b, I'd take the volume with just the outer radius then I'd use ρgV=mg so ρV=m where V is the volume I just calculated and m is the mass of the sphere from the previous part and solve for ρ?