Loudness of sound question

Ryker

1. The problem statement, all variables and given/known data
The speaker receives 10W of electrical power from the amplifier, 4% of which it transforms into sound flow, propagating into a half-space (in front of the speaker) indiscriminately in all directions. How loud is the sound 10m from the speaker?


2. Relevant equations
[tex]L_\mathrm{I}=10\, \log_{10}\left(\frac{I_1}{I_0}\right)\ \mathrm{dB} \,[/tex]
[tex]I = \frac{W}{S}[/tex]


3. The attempt at a solution
The solution is pretty easy to get if you just plug the data into the equations, taking

[tex]S = 4\pi r^{2}[/tex]

But that's the thing I don't quite get. If all of the power that the speaker emits is transformed into sound that only propagates in a half-space, why isn't [tex]S = 2\pi r^{2}[/tex]? I mean, isn't that the point of a speaker, so as to curtail the drawback of sound propagating in all directions and directing its power into only the desired one, thus making it appear louder to our ears?