A wooden toy is a cube of edge 14 cm with a hemisphere of the largest possible radius fixed centrally on its top face. Find the total surface area of the toy in ${\text{cm}}^2$. Take π = 22/7.

The biggest hemisphere on a 14 cm face has radius 7 cm. The cube shows $6\times 14^2=1176{\text{cm}}^2$, but the circle of contact, π$r^2=154{\text{cm}}^2$, is hidden under the hemisphere, while the hemisphere adds its curved surface 2π$r^2=308{\text{cm}}^2$. Total $=1176-154+308=1330{\text{cm}}^2$. (Adding 308 without removing the covered circle gives $1484{\text{cm}}^2$; adding the whole surface of a solid hemisphere, 3π$r^2=462{\text{cm}}^2$, counts the flat face that is glued down and gives $1638{\text{cm}}^2$; $1176{\text{cm}}^2$ ignores the hemisphere.)