A length of metal tubing is 20 cm long. Its outer radius is 5 cm and its inner radius is 4 cm, and both ends are open. What is the total surface area of the tube, counting the outside, the inside and the two flat rims? (Leave the answer in terms of π.)

There are four surfaces. Outer curved = 2π $x5\times 20=200$π. Inner curved = 2π $x4\times 20=160$π. Each end is a flat ring of area π$(5^2-4^2)=9$π, and there are two of them, adding 18π. Total = 200π + 160π + 18π = 378π sq cm. The trap 360π counts only the two curved surfaces and leaves the rims bare; 200π gives the outside alone, as though the tube were solid; 218π keeps the outside and the rims but forgets that a tube can be seen down the inside as well.