We can start by using the density of copper to find the volume of the ingot:
density = mass/volume
volume = mass/density
volume = 57 kg / 8.94 g/cm³
volume = 6,386.85 cm³
Next, we can use the formula for the volume of a cylinder to find the length of wire that can be produced:
volume of wire = πr²l
where r is the radius of the wire and l is its length.
The radius of the wire is half of the diameter, so:
r = 9.50 mm / 2 = 4.75 mm = 0.475 cm
We need to convert the length of the wire to meters, so we will use the conversion factor 1 m = 100 cm.
volume of wire = π(0.475 cm)²l
l = volume of wire / [π(0.475 cm)²]
l = 6,386.85 cm³ / [π(0.475 cm)²]
l = 6,386.85 cm³ / 2.2416 cm²
l = 2,848.79 cm
l = 28.49 m (rounded to two decimal places)
Therefore, a length of wire of approximately 28.49 meters can be produced from the given ingot of copper.