How many gallons of water are in a 10ft dia x 4ft deep swimming pool?

Volume of a cylinder is pi * r (radius) squared * height = 3.14159 * 4 * 20 = 251.3274 cubic feet. 7.48052 gallon of water per cubic foot. Therefore 1880.0597 gallons I assume you mean 4 foot diameter circle. If you meant circumference then the formula changes. Since you know the circumference (2 pi r) you need to calculate the area (pi r squared) Therefore 4 = 2 pi r calculating radius r = 4 / 2 pi. = .6366198. Substituting r above you get 25.4648 cubic feet or 190.4899 gallons