Question

An electric hoist is used to lift a piece of
equipment. The diameter of the drum on the
hoist is d = 10 in, and the equipment must be
raised s = 3 ft.
Find the number of degrees through which
the drum must rotate.
Answer in units of ◦

Answer 1

3 ft = 36 inches

C = 10 pi

36/10pi = now many rotations are needed; and multiply that by 360

Answer 2

412 degrees if its right, a little more

Answer 3

@amistre - yep, I agree. A little more explanation behind the answer:
Imagine there is rope wrapped around the drum, and the bottom of the rope is attached to the piece of equipment. If the drum rotates 360 degrees, you will wrap pi*D rope around the drum's circumference.

Since we don't know how much we're going to wrap, the equation is a little more general.
L = pi*D*(x/360)
L = Length of rope = 3 ft = 36 inches
D = Diameter of Drum = 10 inches
x = degrees of rotation

36 inches = pi*10inches*(x/360)
= 412.5 degrees