A rope is wound 50 times round a c ylinder of radius 25cm .how long is the rope(use pie as 22/7
the cylinder has circumference 2πr = 50π
so, 50 times around would be 2500π cm
Naturally, the rope would have to be somewhat longer, because either
(a) the coils lie side-by-side, so the shape is really a helix
(b) the coils overlap, meaning that the circumference grows by the diameter of the rope for each overlap.
To find the length of the rope wound around the cylinder, we need to calculate the circumference of the cylinder and then multiply it by the number of times the rope is wound.
The formula for the circumference of a cylinder is:
C = 2πr
Where:
C is the circumference,
π (pi) is a mathematical constant approximately equal to 3.14159,
r is the radius of the cylinder.
Given that the radius (r) of the cylinder is 25 cm, we can substitute this value into the formula:
C = 2 * (22/7) * 25
C = 2 * (3.142857143) * 25
C = 157.1428571 cm
Now, multiply the circumference by the number of times the rope is wound, which is 50:
Length of rope = 157.1428571 cm * 50
Length of rope = 7857.142856998 cm
Therefore, the length of the rope wound around the cylinder is approximately 7857.14 cm.