A string wound four times around a rod

Question

A string is wound evenly around a cylindrical rod, making exactly four complete turns as it goes from one end of the rod to the other. The rod is 12 cm long and its circumference is 4 cm.

How long is the string?

Accepted Answer

20 cm. Unroll the cylinder. The curved surface of the rod, laid flat, is a rectangle 12 cm tall (the rod's length) and 4 cm wide (its circumference). Each turn of the string climbs one quarter of the rod's length, 3 cm, while travelling once around, which on the flat rectangle is 4 cm across. So each turn is the diagonal of a 3 cm by 4 cm rectangle. Pythagoras. That diagonal has length the square root of (3 squared + 4 squared) = 5 cm. Four turns: 4 × 5 = 20 cm. One diagonal instead of four. Alternatively, tape four copies of the 4 cm wide rectangle side by side to make a strip 16 cm wide and…

A string wound four times around a rod

Your answer

Discussion

Learn the concepts

Related questions