The cage will drop 18.84m for each single rotation of the drum.
It is given that the diameter of the mine winch, d= 6 m.
We can calculate that how far the cage will drop for each single rotation of the drum by using the formula of the circumference.
Circumference, c = 2πr
where,
r = d/2 (radius of the mine winch)
r = 6/2
⇒ r = 3m
Circumference, c = 2πr
⇒ c = 2π×(3)
⇒ c = 6π
⇒ c = 18.84m
Hence, the cage will drop 18.84m for each single rotation of the drum.
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