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8 August, 17:34

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?

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  1. 8 August, 18:18
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    a) # lap = 301.59 rad, b) L = 90.48 m

    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
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