A vessel is an upside-down cone of height 8 cm and radius 5 cm, filled to the brim with water. Spherical lead shots of radius 0.5 cm are dropped in until one-fourth of the water has spilled over. How many shots were dropped?

Water held = (1/3)π × $25\times 8=200$π/$3{\text{cm}}^3$, so the spilt quarter = 50π/$3{\text{cm}}^3$ — and that equals the total volume of the shots. Each shot = (4/3)π$(0.5{)}^3$ = π/$6{\text{cm}}^3$. Number = (50π/3) ÷ (π/6) = 100. (Using the whole cone instead of a quarter of it gives 400; dropping the 1/3 in the cone gives 300; treating a shot as a hemisphere gives 200.)