A sphere made of a material of specific gravity 8 has a concentric spherical cavity and just sinks in water. Calculate the ratio of the radius of the cavity to that of the outer radius of the sphere.

Explanation

Let the radius of the sphere be R and that of the cavity be r. Then, since the sphere just sinks in water,
`4/3 pi (R^3 - r^3) rho g = 4/3 pi R^3 rho_w g`
`1 - (r/R)^3 = (rho_w)/(rho) = 1/8`