A cylindrical vessel of radius 5 cm is partly filled with water. A solid metal sphere of radius 3 cm is dropped in and sinks completely. By how many centimetres does the water level rise?

The rise happens because the sphere pushes its own volume of water up. Sphere = $\frac{4}{3}\pi (3{)}^3=36\pi {\text{cm}}^3$. This becomes a cylinder of water of radius 5 cm and height $x$, so $\pi (25)x=36\pi$, giving $x=36/25=1.44$ cm. Notice π cancels, so no value of π is needed. 0.72 uses $\frac{2}{3}\pi r^3$ (a hemisphere) for the ball; 4 uses the ball's own radius 3 cm as the vessel radius; 2.88 doubles the answer.