Was looking back through my college notes and came across this question. I must have solved it back then, but just get stamped now.
A fluid storage tank has an external ladder that goes around its lateral surface completing 2/3 of a revolution. The height of the tank is 15m and its radius is 2m. The handrail of the ladder is 1/2 m away from the tank. Estimate the length of the handrail.
Imagine "uncurling" the wall of the tank so that it is a rectangular sheet, and so the ladder is straight instead of spiraling.
The handrail is the hypotenuse of a right triangle with legs $15$ meters and $\frac{2}{3} \cdot 2 \pi (2.5)$.