If the mine winch drum diameter is 6m calculate how the cage will drop for each single rotation of the drum use the formula C=TTr

You have the formula, though it is incorrect, so fix it and use it.

If you don't know why to use the formula, you just don't understand the problem.
One turn of the wheel uses up enough rope to wrap around the circumference of the drum.
The formula gives you that circumference.

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To calculate how far the cage will drop for each single rotation of the drum, we can use the formula C = T * π * r, where C is the circumference of the drum, T is the number of rotations, and r is the radius of the drum.

In this case, the diameter of the drum is given as 6 meters. We can find the radius by dividing the diameter by 2:

Radius (r) = Diameter / 2 = 6m / 2 = 3m

Now, we can substitute the given values into the formula:

C = T * π * r

C = T * 3.14 * 3m

To get the distance the cage will drop for each single rotation, we need to find the circumference of the drum. The formula for the circumference of a circle is C = 2 * π * r.

Circumference (C) = 2 * π * r = 2 * 3.14 * 3m = 18.84m

Therefore, for each single rotation of the drum, the cage will drop a distance of 18.84 meters.