Question

Electrical wire with a diameter of .5 cm is wound on a spool with a radius of 30 cm and a height of 24 cm.

a) Through how many radians must the spool be turned to wrap one even layer of wire?
b) What is the length of this wound wire?

Answer 1

a) # lap = 301.59 rad , b) L = 90.48 m

Step-by-step explanation:

a) Let's use a direct proportions rule (rule of three). If one turn of the wire covers 0.05 cm, how many turns do you need to cover 24 cm

# turns = 1 turn (24 cm / 0.5 cm)

# laps = 48 laps

Let's reduce to radians

# laps = 48 laps (2 round / 1 round)

# lap = 301.59 rad

b) Each lap gives a length equal to the length of the circle

L₀ = 2π R

L = # turns L₀

L = # turns 2π R

L = 48 2π 30

L = 9047.79 cm

L = 90.48 m