The Greek Theatre in the town of Taormina in Sicily has a spectacular view of the bay and of Europe’s highest volcano, Etna. The theatre itself dates to the third century BCE and although it's called the “Greek” Theatre, is largely the work of the Romans (the giveaway is that it is predominantly brick-built).
It’s regularly used as a concert venue, and the descriptive material suggests that it originally had a capacity of 5000. Is this claim credible? Let’s see if we can make an independent estimate of our own to compare.
As the image shows, the seating is arranged in sections, seven of them in total. So, trying to arrive at our own estimate of the capacity, we can tackle the simpler task of forming an idea of the capacity of one of those sections (and then later multiply by seven). Let’s take a closer look at one of the sections:
Counting the rows of seats (the lower ones are original stone, the upper ones are wooden bleachers), we get to 26 rows of seats currently in place. But there is some evidence of further, unrestored structure lower down, so we can guess that there might have been a further block of perhaps 12 rows there, for a total of 38 rows.
How many people might sit on one of those rows? More on the back rows, fewer in the front, but a reasonable figure for one of the middle rows might be 15 people.
So, we have 7 sections of 38 rows, each accommodating (on average) 15 people. Multiply those together to get 3990. It’s the right order of magnitude, but somewhat short of the 5000 claimed: perhaps that’s an optimistic claim?
But hold on! Those seven sections don’t make a complete semicircle. There is, in fact, on each side, space for a further section which would bring the total to nine sections, and that would make the total number of seats 5130. We can probably conclude that 5000 is a fair estimate.