The character 球 means ball and is composed of

  1. 王 meaning king and
  2. 求 meaning demand.

Where does this composition come from? Did a king ask for a ball?

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    @jogloran gave a great answer, but I also wanted to point out that in general, most characters should not be analyzed via the meaning of their components. In fact over 90% of characters are phono-semantic compounds, in which one component hints at the meaning while the other hints at the pronunciation, as is the case here. – Claw May 21 '13 at 19:30

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

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