A hollow, spherical glass has an inner radius of R and an outer radius of 1.2R. The density of the glass is d. What fraction of the shell is submerged when it floats in a liquid of density ρ = 1.5d (1.5 times the density of the glass)? (Assume the interior of the shell is a vacuum.)
Volume Sphere = (4/3)πr^3
The Attempt at a Solution
I attempted to set the weight of the water displaced equal to the weight of the shell. (Sum of forces = 0, Bouyont Force - Mass of Shell = 0, BF = Mass of Shell. For weight of shell I used W=ρgh with the volume being the volume of a sphere with r of 1.2R minus volume of a sphere with r of R. For the volume of water displaced I just used some variable fraction multiply by the volume of a sphere equation. ds and Rs then cancel out. I know the answer I'm supposed to get is 0.28, but I keep getting 0.48. Any insight towards a full solution would be hugely appreciated!