A cylindrical bucket with base radius 15 cm is filled with water up to a height of 20 cm.

Let h cm be the increase in the level of water.
Radius of the cylindrical bucket = 15 cm
Height up to which water is being filled = 20 cm
Radius of the spherical ball = 9 cm
Now, volume of the sphere = increased in volume of the cylinder

$\Rightarrow \frac{4}{3} \pi \times 9^{3}=\pi \times 15^{2} \times h$

$\Rightarrow h=\frac{4 \times 729}{3 \times 15 \times 15}=\frac{4 \times 27}{25}=4.32 \mathrm{~cm}$

∴ The increase in the level of water is 4.32 cm.