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?

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