A cylinder 90 cm high has a circumference of 24 cm. A string makes exactly 5 complete turns around the cylinder while each of its two ends touch the cylinder's top and bottom respectively.

How long is the string?

If you imagine a sheet of paper covering the cylander like a soup-can label, and the position of the string marked on the label, then when you remove the label, you will find it to be a 90 x 24 rectangle with 5 lines marked on it. Each line will go from a point at one end of the rectangle to a point 18 cm higher at the other end. The length of each of these lines is √(24² + 18²) but since 24 and 16 are both divisible by 6, this simplifies to 6√(4² + 3²) = 6√(5²) = 30. since there are five line segments, the total length is 5(30) = 150 cm, which is the length of the string

Posted by TomM on 2002-08-09 14:28:41