Did a king ask for a ball? How did 王 + 求 become 球?
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