A glass sphere has a cavity inside it. whhen placed in water, it floats with `20` of its volume above the water surface. Find the volume of the cavity as a fraction of total volume (density of glass `=2.5g//"cc")`.

Explanation

Let the total volume of the sphere be `V`.
Weight of the sphere `=` Buoyant force
`implies` Mass of glass `xxg=80/100Vxx1xxg`
`implies` Volume of galss `xxd=(80V)/100`
If the volume of the cavity is `v`, then the volume of the galss is `(V-v)`,
`(V-v)d=0.8Vimplies(V-v)/V=0.8/2.5`
`implies(V-v)/V=0.32impliesv/V=0.68`
Hence, volume of the cavity of `68%` of total volume.
`implies` Volume of glass `xxd=(80V)/100`
If the volume of the cavity is `v`, then the volume of te glass is `(V-v)`,
`(V-v)d=0.8Vimplies(V-v)/V=0.8/2.5`
`implies(V-v)/V=0.32impliesv/V=0.68`
Hence, volume of the cavity is `68%` of the total volume.