How is this sentence a paradox? "My voice must have carried, for silence fell on the whole room like a clap." I know it is a paradox because it...

You have a couple of polar opposites at work here, making this sentence a definite paradox. You cannot have silence if a voice is present. That much is evident. However, if you look further, you will see that the author says that silence fell on the room like a clap, also something that makes noise. Whether it's the clapping of hands or boards, a clap is definitely a noisemaker, and noise prevents silence.

Teachers will tell you that almost everyone has had an experience where they have said something extreme or shocking, and the immediate result is silence from everyone else in the room where the comment took place. It sounds as if this is the context in which this quote is delivered -- someone just said something that made everything else fall utterly silent. The way the quote is presented makes it paradoxical, however.