Since the height and radius of the bucket and the scoop are the same, the volume of the bucket and the scoop can be calculated as follows:
V_bucket = π * r^2 * h = π * r^2 * r = π * r^3
V_scoop = (1/3) * π * r^2 * h = (1/3) * π * r^2 * r = (1/3) * π * r^3
Now that we have the volumes of the bucket and the scoop, we can find the number of scoops it would take to fill the bucket 15 times:
V_bucket * 15 = 15 * π * r^3
V_bucket * 15 / V_scoop = 15 * π * r^3 / (1/3) * π * r^3 = 45
So it would take 45 scoops of water to fill the bucket 15 times.