Answer:
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
