Question

A piece of string is wound tightly round a cylinder for 20 complete turns, the length of the string is found to be 3.96m, calculate the diameter of the cylinder in cm.

Answer 1

First, we need to find the length of string that makes one complete turn around the cylinder. This is equal to the circumference of the cylinder, which is given by:

C = 2πr

where r is the radius of the cylinder.

We know that the string makes 20 complete turns around the cylinder, so the total length of string used is 20 times the circumference:

L = 20C = 40πr

We are given that this is equal to 3.96m, so we can solve for r as follows:

40πr = 3.96

r = 3.96 / (40π) = 0.01m

Finally, we can find the diameter of the cylinder by doubling the radius:

d = 2r = 0.02m = 2cm

Therefore, the diameter of the cylinder is 2cm.