Question

Copper has a density of 8.94 g/cm3 . If a factory has an ingot of copper with a mass of 125 pounds and the ingot is drawn into a wire with a diameter of 9.50 mm, how many feet of wire can be produced? (454 grams = 1 pound)

Answer 1

Answer: The length of copper wire is 295.68 feet.

Explanation:

To calculate volume of a substance, we use the equation:

$\text{Density of substance}=\frac{\text{Mass of substance}}{\text{Volume of substance}}$

Density of copper = $8.94g/cm^3$

Mass of copper = 125 pounds = 56750 g   (Conversion factor: 1 pound = 454 g)

Putting values in above equation, we get:

$8.94g/cm^3=\frac{56750g}{\text{Volume of copper}}\\\\\text{Volume of copper}=6347.87cm^3$

The volume of copper wire is $6347.87cm^3$. The copper wire is in the shape of cylinder.

The equation used to calculate the volume of cylinder is:

$V=\pi r^2h$

where,

V = volume of copper wire = $6347.87cm^3$

r = radius of the copper wire = $\frac{d}{2}=\frac{0.95cm}{2}=0.475cm$      (Conversion factor: 1 cm = 10 mm)

h = length/ height of the copper wire = ?

Putting values in above equation, we get:

$6347.87cm^3=(3.14)\times (0.475)^2\times h\\\\h=8960cm$

Converting this value of length of copper wire into feet, we use the conversion factor:

1 cm = 0.033 foot

So, $8960cm=0.033\times 8960=295.68ft$

Hence, the length of copper wire is 295.68 feet.