To get a rough estimation of the size of Antarctica, we think of it as a circle with a diameter equal to the width of USA. See—now we've made a connection between something you don't really have a feeling for to something you might be familiar with. So, how far is it across the USA? Let's say it has a width of width of around 3,000 miles (4,800 km). So, if we approximate this as the diameter of a circular Antarctica, the surface area would be:Forgive me, but I'm going to cheat a little bit. Since I really don't know if this value is legit or crazy, I'm going to take a peak at the Wikipedia Antarctica page. Oh great—I'm reasonably close. I feel better now. But wait! There's one other tough thing to estimate—the average depth of the ice sheet at the South Pole. Well heck. I already looked at the page and I see that the average ice thickness is 1.9 km. It's all for the best. There's no way I would have guessed it's that thick. That's a crazy amount of ice.
So now, we can visualize this ice sheet as a giant cylinder—maybe more like a hockey puck shaped cylinder. I can calculate the volume as the area of the base (a circle) multiplied by the height. I'm going to keep the measurements in units of meters just to make things easier going forward.