A cylinder 72 cm high has a circumference of 24 cm A string makes exactly 4 complete turns round the cylinder while its two ends touch the cylinder's top and bottom How long is the string in cm?

Answer 1

If you open the cylinder it becomes a rectangle. Because the string encircles the cylinder four times while it moves up the cylinder's height, it then moves around 24cm x 4 = 96cm of "horizontal" (level with the base of the cylinder or the rectangle that is formed) distance and 72cm of the "vertical" (up the cylinder) distance. These distances form a right-angled triangle. By using Pythagoras' theorem, a2 + b2 = h2, where 'h' is the hypotenuse of the triangle and the length of the string, we can calculate the actual length of the string as thus: h2 = a2 + b2 = 722 + 962 = 5184 + 9216 = 14400 h = the square root of 14400 = 120cm. ---- Another method uses the same idea, but forms four identical triangles; one for each turn of the string around the cylinder. When the cylinder is unrolled into a rectangle as before, each triangle has a horizontal distance of 24cm and a vertical distance of 72cm/4 = 18cm. Using Pythagoras' theorem again, we can calculate the length of the hypotenuse of one of these triangles, which works out as 30cm. We have four such triangles, so multiplying that by 4 gives an answer of 120cm, just as before.