The answer to the question: The capitol building is in Austin. But the city of Austin is the capital of Texas. If you are speaking of the building, it is spelt* “capitol”. But the city is spelt “capital”.
Mnemonic: You may remember this as Austin is the capital with an “a”, but the old office building is spelt with an “o”!
mnemonic = something to aid in memory (don’t pronounce the “m” in this crazy word!)
“Spelt” or “spelled”: Either is correct. When I grew up, it was “spelt” and I think it sounds better, so I prefer it! But the more common way is “spelled”.