A solid sphere and a hollow sphere of same external radius and made of same material are floating in water. Solid sphere has three fourths of its volume submerged and the hollow sphere is half submerged. What fraction of the volume of hollow sphere is hollow?

The solid sphere floats $$\frac{3}{4}$$ submerged, so the material's density is $$\frac{3}{4}$$ that of water. If the hollow sphere has outer volume $$V$$ and material volume $$V_m$$, its weight equals the buoyancy on half its volume, so $$\frac{3}{4}V_m = \frac{1}{2}V$$ and $$V_m = \frac{2}{3}V$$. The hollow part is $$1 - \frac{2}{3} = \frac{1}{3} \approx 0.33$$ of the volume.