A cylindrical tin of radius 10.5 cm and height 12 cm is to be wrapped once round its curved surface with a rectangular paper label, edge to edge and with no overlap. Find the area of the label in ${\text{cm}}^2$. Take π = 22/7.

Unrolled, the label is a rectangle as tall as the tin and as long as the rim: area = 2πrh = $2\times (22/7)\times 10.5\times 12=792{\text{cm}}^2$. (Using πrh instead of 2πrh gives $396{\text{cm}}^2$; adding the two circular ends gives the total surface $792+693=1485{\text{cm}}^2$, but a label wraps only the side; using the diameter 21 cm as the radius gives $1584{\text{cm}}^2.$)