A heavy box is attached to a circular pulley to hoist it up

A heavy box is attached to a circular pulley to hoist it up for cargo loading. If the radius of the pulley is 7 inches, through how many degrees must it rotate (counterclockwise) in order to move the box up 7 feet? Round your answer to the nearest degree Be careful of units! A plot of land is bounded on one side by a highway that curves. Assuming the curve is the arc of a circle with the central angle shown in the figure, what is the area of the entire plot in acres? Round your answer to the nearest acre.

Solution

1 radius of pulley = 7 inches

the distance that weight is raised is equal to arc length

1 feet = 12 inches

so, 7 feet = 84 inches

arc length = radius * angle

84 = 7 * angle

angle = 84/7 = 12 * 180 / pi

= 688 degrees approx