A solid wooden cylinder of radius 10.5 cm and height 20 cm is sawn into two identical halves by a straight cut running down through its axis. What is the total surface area of one half, in square cm? (Use π = 22/7.)

One half has three kinds of face. Half the curved surface = π$rh=(22/7)\times 10.5\times 20=660$ sq cm. Two semicircular ends together make one full circle = π$r^2=346.5$ sq cm. The cut also exposes a flat rectangle of $2r$ by $h=21\times 20=420$ sq cm. Total = 660 + 346.5 + 420 = 1426.5 sq cm. The trap 1006.5 forgets the newly exposed rectangle, which is the whole point of cutting; 1080 forgets the two semicircular ends; 2013 is the untouched cylinder's surface, 2π$rh+2$π$r^2$.