How many gallons of water would an 20' round by 48 deep swimming pool hold?

If the 20' is the diameter of the pool (radius 10 feet) and the depth is 48 inches (4 feet) the volume of the pool in cubic feet would be found by the formula pi x r2 x h - with pi as 3.14159, r2 as 100 and h as 4

... which gives 1256.636 cubic feet

1 cubic foot of water = 7.4805195 US gallons (or 6.2288355 Imperial gallons), so 1256.636 cubic feet would be 9,400.2901 US gallons (or 7,827.3789 Imperial gallons)

-=-=-=-

If, however, the 20' is the circumference, then the radius would be just over 3.18 feet and the formula becomes 3.14159 x 10.13 x 4

... which gives 127.297 cubic feet

That converts to 952.25 US gallons or 792.9 Imperial