Fluid Mechanics

[Honda47]

I'm doing some practice problems because I have a final tomorrow. I ran across this problem and I haven't seen an equation or example like it in our textbook. If you could give me a little direction I'd appreciate it I probably won't have one like it on the test but I'd still like to figure it out.

A spherical aluminum ball of mass 1.26 kg contains an empty spherical cavity that is concentric with the ball. The ball just barely floats in water. Calculate (a) the outer radius of the ball and (b) the radius of the cavity.

Thanks

[Astronuc]

You can calculate the radius of the sphere from the volume of the sphere, which you get by dividing the density of water by the mass of the ball. Why?

Because in order to barely float, the smear density must be the same as water (1 gm/cc).

Then since you know the real density of all (~2.7 g/cc), you can find the actual volume of Al

Then the volume of the cavity is just the difference in volumes.

Then find the radius of the cavity.