Ooh, I caught one in time! Given the shape of your pool, it'll be relatively easy to calculate its volume. But to double check...
Keep a close eye on the plasterers, because they'll start your fill the minute they finish. Just before they do, go take a picture of your city's water meter. Minimize water use in the house and yard (showers, toilet flushes, laundry, dishwasher, sprinklers, irrigation, etc). When the water level makes it halfway up the skimmer opening, turn off the fill and take another snap of the water meter. The difference between those two numbers will be your pool's volume, give or take a percentage point or two. The less water you use during the fill, the more accurate will be your number.