A cylindrical hole of radius 3.5 cm is bored straight through a solid wooden cube of edge 10 cm, from the centre of one face to the centre of the opposite face. Find the volume of wood left, in ${\text{cm}}^3$. Take π = 22/7.

The hole is a cylinder of radius 3.5 cm whose length is the edge of the cube, 10 cm: volume = $(22/7)\times 12.25\times 10=385{\text{cm}}^3$. The cube holds $10^3=1000{\text{cm}}^3$, so the wood left $=1000-385=615{\text{cm}}^3.(385{\text{cm}}^3$ is the wood removed, not what is left; $1000{\text{cm}}^3$ ignores the hole; $230{\text{cm}}^3$ subtracts the same hole twice, but one bore makes one tunnel.)