This JPG picture
The String on the Cylinder
comes
Contributed by Raymond Lu
From: Puzzles And Brain Teasers
Source
http://www.syvum.com/cgi/online/serve.cgi/contrib/teasers/string1.tdf?0
Solution:
http://www.syvum.com/cgi/online/serve.cgi/contrib/teasers/string1.tdf?0
Solution:
The figure alongside illustrates how the cylinder can be unrolled into a rectangle for the case where the string makes exactly 4 complete turns.
For the given problem, the cylinder can be unrolled into a rectangle with dimensions 72 cm by 16 cm. The string thus creates 6 diagonal lines whose measure can be found out by considering the 6 right triangles they can form:
- the base of the triangle is 16 cm and the height is 1/6 of 72 or 12 cm.
- from these, we can get the measure of one diagonal line as 20 cm [i.e., (162 + 122) 1/2] by using the Pythagorean theorem.
- therefore, the whole string measures 120 cm (i.e., 6 x 20 cm).