The largest possible cylinder is cut from a solid wooden cube of edge 14 cm. Find the ratio of the volume of the cylinder to the volume of the cube. Take π = 22/7.

The cylinder's diameter cannot beat the cube's edge, so $r=7$ cm, and its height is the full edge, 14 cm. Cylinder = $(22/7)\times 49\times 14=2156{\text{cm}}^3$; cube = $14^3=2744{\text{cm}}^3$. Ratio = 2156 : 2744 = 11 : 14 (both divide by 196). Since the cylinder sits inside the cube its share must be less than one, so 14 : 11 cannot be right.