To predict the sinking/floating behavior of a spherical object, you could determine its density.
Step 1. Determine its mass on a suitable balance.
Step 2. Determine its volume
Either
Measure its circumference. C = 2πr, so you can calculate r
or
Measure its diameter. d = 2r, so you can calculate r
Then
V = ⁴/₃πr³ , so you can calculate its volume.
Step 3. Calculate its density (D).
Density = mass/volume
If D < 1 g/cm³, the object will float in water. If D > 1 g/cm³, the object will sink.