A wire is bent into a square of side 33 cm. It is then straightened and bent again into a circle. By how many ${\text{cm}}^2$ does the enclosed area increase? Take π = 22/7.

The wire keeps its length: $4\times 33=132$ cm. For the circle, 2π$r=132$ gives $r=(132\times 7)/44=21$ cm and area = $(22/7)\times 441=1386{\text{cm}}^2$. The square enclosed $33^2=1089{\text{cm}}^2$, so the gain $=1386-1089=297{\text{cm}}^2$. (1386 and 1089 are the two areas themselves, not the increase; solving π$r=132$ instead of 2π$r=132$ gives $r=42$ and a wrong gain of $4455{\text{cm}}^2.$)