Question

spherical aluminum ball of mass 1.22 kg contains an empty spherical cavity that is concentric with the ball. The ball just barely floats in water.Calculate the radius of the cavity.

Answer 1

R = outer radius
r = inner radius (of spherical cavity)

Sphere weight = buoyancy force

(4/3) pi (R^3 - r^3)*(density of Al)*g
= (4/3) pi R^3 * (density of water)*g

(4/3) pi R^3 * (density of water)
= 1.22 kg

(Use the second equation to solve for R)

The (4/3) pi g cancels out in the first equation.

1 - (r/R)^3
= (water density)/(Al density)

Look up the densities and solve