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29 October, 14:45

A factory has a solid copper sphere that needs to be drawn into a wire. The mass of the copper sphere is 76.5 kg. The copper needs to be drawn into a wire with a diameter of 9.50 mm. What length of wire, in meters, can be produced?

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  1. 29 October, 15:18
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    120.125 m

    Explanation:

    Density = Mass/volume

    D = m/v ... Equation 1.

    Where D = Density of the solid copper sphere, m = mass of the solid copper sphere, v = volume of the solid copper sphere.

    Making v the subject of the equation,

    v = m/D ... Equation 2

    Given: m = 76.5 kg,

    Constant: D = 8960 kg/m.

    Substituting into equation 2

    v = 76.5/8960

    v = 0.0085379 m³

    Since the copper sphere is to be drawn into wire,

    Volume of the copper sphere = volume of the wire

    v = volume of the wire

    Volume of wire = πd²L/4

    Where d = diameter of the wire, L = length of the wire.

    Note: A wire takes the shape of a cylinder.

    v = πd²L/4 ... equation 3.

    making L the subject of the equation,

    L = 4v/πd² ... Equation 4

    Given: v = 0.0085379 m³, d = 9.50 mm = 0.0095 and π = 3.14

    Substitute into equation 4

    L = 4*0.0085379 / (3.15*0.0095²)

    L = 0.0341516/0.0002843

    L = 120.125 m.

    L = 120.125 m

    Thus the length of the wire produced = 120.125 m
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