A solid cylinder of radius 7 cm and height 20 cm is cut into two equal pieces by a plane containing its axis. Find the total surface area of one piece, in ${\text{cm}}^2$. Take π = 22/7.

One piece keeps half the curved surface, πrh = $(22/7)\times 7\times 20=440{\text{cm}}^2$, and two semicircular ends, which together make one full circle, π$r^2=154{\text{cm}}^2$. The cut also creates a new flat rectangle as wide as the diameter and as tall as the cylinder: $14\times 20=280{\text{cm}}^2$. Total $=440+154+280=874{\text{cm}}^2$. (Forgetting the new rectangle gives $594{\text{cm}}^2$, which is exactly half the uncut cylinder's surface — but cutting must ADD area; forgetting the semicircular ends gives $720{\text{cm}}^2$; $1188{\text{cm}}^2$ is the whole uncut cylinder.)