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?

This one was pretty easy. The Thing is 90 high, and the string goes around exactly 5 times. If you unroll a cylinder, you have a rectangle. The string would effectively go corner to side 5 times, so think of your 90 x 24 cylinder as 5 rectangles and the string goes corner to corner. Applying pyth theorem, the sides of each is 18 x 24, so squaring each of those and summing comes to 324+576=900. the squareroot of that is 30. You have 5 of these, so the string is 150cm.

Cheers!

Posted by Lawrence on 2003-08-27 20:16:52