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.
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.
To find the diameter of the cylinder, we need to use the formula for the circumference of a cylinder, which is C = 2πr, where C is the circumference and r is the radius of the cylinder.
Since the string is wound tightly around the cylinder for 20 complete turns, the length of the string will be equal to 20 times the circumference of the cylinder.
Given that the length of the string is 3.96m, we can set up the equation:
20C = 3.96
To find the circumference C, we divide both sides of the equation by 20:
C = 3.96 / 20
C = 0.198m
We know that C = 2πr, so we can set up a new equation:
0.198 = 2πr
To find the radius r, we divide both sides of the equation by 2π:
r = 0.198 / (2π)
Now, we can calculate the radius:
r ≈ 0.198 / (2 x 3.14)
r ≈ 0.198 / 6.28
r ≈ 0.0316m
Finally, to find the diameter of the cylinder, we multiply the radius by 2:
d = 2 x r
d ≈ 2 x 0.0316
d ≈ 0.0632m
To convert the diameter to centimeters, we multiply by 100:
d ≈ 0.0632 x 100
d ≈ 6.32 cm
Therefore, the diameter of the cylinder is approximately 6.32 cm.