When the water level rises 1 in, the amount of water in the tank increases by : 10 x 15 x 1 = 150 (in³)

The volume of each sphere is : \(\dfrac{4}{3}\pi\left(\dfrac{1}{6}:2\right)^3=\dfrac{1}{1296}\pi\) (in³)

The answer is : \(150:\dfrac{1}{1296}\pi\approx61900\) (spheres)