<PRE><B>Question 865352</B>
A cable with one end attached to a bucket at the bottom of a mine shaft is being wound around a cylindrical drum 12 feet in diameter which is turning at the rate of 24 rpm. assuming the hoist is raising the bucket from the bottom of the shaft to the surface in nine minutes and thirty four seconds, calculate the depth of the shaft accurate to the nearest ten feet. (please explain) 

If the drum rotates once the bucket will rise by 2*pi*r feet

radius of drum = 6 feet

so circumference = 12 pi

In one minute it makes 24 revolutions

In one minute the bucket will come up by 24 * 12 pi feet



so in 9 mins 34 seconds it will cover ?

9 34/60 = (287/30)

It will cover {{{(287/30) *( 24*12 * 3.14)}}}
=8651.328

= 8651 feet

the depth is 8651 feet
 

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