posted by jenna on .
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.
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