A 3 year old child needs between 10 to 12 hours of sleep to be fully rested.
Some 3 year olds may get cranky or upset and need a nap during the day of at least 1 hour or even a 30 minute nap.
It all depends on the 3 year old and how tired they are.
When I was 3 years old I would take a nap for 30 minutes and then get up and run around and play or whatever and then take another 30 minute nap an hour or so later.
Sometimes it would be hard to get me to take a nap and other times I could take a nap just about anywhere.
I have some funny pictures of me as a 2 and 3 year old taking naps in the oddest of places where I could not imagine being able to sleep now.