A brass washer is the piece of metal lying inside a 120° sector of a circle of radius 9 cm but outside a circle of radius 6 cm drawn about the same centre. What is the area of the washer, in square cm? (Use π = 3.14.)

Take the 120° slice of each circle and subtract: area = (120/360) $x$ π$(R^2-r^2)=(1/3)\times 3.14\times (81-36)=(1/3)\times 3.14\times 45=47.1$ sq cm. The trap $84.78=(1/3)\times 3.14\times 81$ is the outer slice with the hole never removed; $9.42=(1/3)\times 3.14\times 9$ uses $(R-r{)}^2=9$ in place of $R^2-r^2=45$, and those are quite different quantities; $141.3=3.14\times 45$ is the full ring right round the centre, forgetting that only 120° of it is brass.