From a solid cylinder of radius 7 cm and height 21 cm, the largest possible right circular cone standing on the same base and having the same height is carved out. What is the volume of the remaining solid, in cubic cm? (Use π = 22/7.)

The cylinder is $(22/7)\times 49\times 21=3234$ cubic cm, and a cone on the same base with the same height holds exactly one third of it, $(1/3)\times 3234=1078$ cubic cm. What remains = 3234 - 1078 = 2156 cubic cm, i.e. two thirds of the cylinder. The trap 1078 reports the piece REMOVED rather than what is left; 3234 is the untouched cylinder; 1617 assumes the cone is half the cylinder instead of a third.