A winch system consists of two interlocking gears, X X\,X and YYY, as shown in the diagram. Gear X X\,X has 15 teeth and is driven by an electric motor. Gear Y Y\,Y has 45 teeth and is coaxially fixed to a cylindrical winch drum of radius R=0.4π m\displaystyle R = \frac{0.4}{\pi}\text{ m}R=π0.4 m, so that they rotate together.
During a lifting operation, Gear X X\,X completes exactly 12 full revolutions.
What is the vertical distance lifted by the load?
1.6 m1.6\text{ m}1.6 m
3.2 m3.2\text{ m}3.2 m
9.6 m9.6\text{ m}9.6 m
28.8 m28.8\text{ m}28.8 m