A solid sphere of radius b is having a concentric cavity of radius a. The sphere floats on the surface of water such that half of its volume sinks in water. Find the relative density of material of the sphere.

• A. \(\frac{{{b^3}}}{{{a^3}}}\)
• B. \(\frac{{{b^3}}}{{{b^3} - {a^3}}}\)
• C. \(\frac{{{b^3}}}{{2\left( {{b^3} - {a^3}} \right)}}\)
• D. \(\frac{{2{b^3}}}{{{b^3} - {a^2}}}\)