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This is just something that always bothered me. Aren't the Uruks portrayed before and during the battle too many to really be only 10k? 10k people aren't really that many, is the capacity of a very small football stadium. To me they look more like 30-50k, especially when Saruman watches them from the balcony, when they march and during the first scene of the battle.
Are there actually more than 10,000 Uruks present at the battle?
Saruman doesn't have 10,000 Uruk-hai but "Tens of thousands", you've misheard what Saruman says.
Gríma: Even if it is breached, it would take a number beyond reckoning, thousands to storm the keep.
Saruman: Tens of thousands.
Gríma: But, my lord, there is no such force.
[Both of them came onto the balcony of the tower. Gríma suddenly sees and hears the enormous armies laid out below in neat rows and is astounded and awed. He continues to hold the extinguished candle aloft as he gapes at the vast army below. A horn is sounded, announcing the appearance of Saruman. A loud cheer is heard from the army. Saruman raises a hand.]
You can hear he says "Tens" in the relevant scene as well:
So yeah there are more than 10,000 present in the army, you just misheard the quote.
Note that when Aragorn relays the information to Théoden he says "Ten thousand strong at least" implying that there isn't only ten thousand but that is the minimum bound. He either didn't stay to keep counting or left to get the news back as quickly as possible. Ten thousand is already a formidable force, no point in carrying on counting when time is of the essence.
Théoden: A great host, you say?
Aragorn: All Isengard is emptied.
Théoden: How many?
Aragorn: Ten thousand strong at least.
Théoden: Ten thousand?!
