A lampshade is a frustum open at both ends, its two rims having radii 18 cm and 10 cm and its slant height being 21 cm. Find the area of sloping material in it, in ${\text{cm}}^2$. Take π = 22/7.

The sloping surface of a frustum is π$l(R+r)=(22/7)\times 21\times (18+10)=66\times 28=1848{\text{cm}}^2$. (Subtracting the radii instead of adding them, π$l(R-r)$, gives $528{\text{cm}}^2$; borrowing the trapezium rule and halving, ½π$l(R+r)$, gives $924{\text{cm}}^2$; $3696{\text{cm}}^2$ doubles, as if the shade were a full cylinder's curved surface.)