A searchlight fixed on a watchtower lights the ground out to a distance of 63 $m$ and swings through an angle of 80°. Find the area lit, in $m^2$. Take π = 22/7.

The lit patch is a sector of radius 63 $m$: area = $(80/360)\times (22/7)\times 63^2=(2/9)\times 12474=2772m^2.(12474{\text{m}}^2$ is the whole circle, which would need a full 360° sweep; $5544{\text{m}}^2$ doubles the sector, as if the beam swung through 160°; 88 $m$ is the length of the arc traced by the far edge of the beam — a length, not an area.)