The character 球 means ball and is composed of
- 王 meaning king and
- 求 meaning demand.
Where does this composition come from? Did a king ask for a ball?
Nope. The radical was simplified from 玉 (jade), originally referring to a polished sphere of jade. 求 is the phonetic component.
For reference, Baxter's Old Chinese reconstruction has 求 *grju, and 球 *grju. In this particular case, 求 has remained a good phonetic for three millennia!
The sense of 'sounding stone made of jade' can be seen in the Kangxi dictionary: http://www.kangxizidian.com/kangxi/0732.gif