How old is Mr. Spock (the character, not the actor) in bintang Trek: The Original Series?

If Kirk was born in 2233 and became captain of the USS Enterprise in 2265 (first episode of the Original Series "Where No Man Has Ever Gone Before" (or a bit later)) and Spock was born in 2230, we can assume that Spock was about 35 years old at the very beginning of the original series.