Question

If the copper is drawn into wire whose diameter is 8.00mm , how many feet of copper can be obtained from the ingot? The density of copper is 8.94 g/cm3.
(Assume that the wire is a cylinder whose volume is V=πr2h, where r is its radius and h is its height or length.)

Answer 1

If the copper is drawn into wire whose diameter is $8.00\mathrm{mm}$, how many feet of copper can be obtained from the ingot? The density of copper is $8.94~\mathrm{g/cm^3}$. (Assume that the wire is a cylinder whose volume is $V = \pi r^2 h$, where $r$ is its radius and $h$ is its height or length.)

Solution:

$V = \pi r^2 h$ and $V = \frac{m}{\rho}$; where $r$ is radius, $h$ is length, $m$ is mass of copper and $\rho$ is density of copper.

Then

$$V = \pi r ^ {2} h = \frac {m}{\rho} \text{ and } h = \frac {m}{\pi r ^ {2} \rho}$$

Let $m$ is 1 kg; $r$ is radius and it is a half of diameter (4.00 mm or 0.004 m); $\pi$ is a constant and is 3.14; and $\rho$ is density (8.94 g/cm³ or 8940 kg/m³).

$$h = \frac {1}{3.14 \cdot 0.004 ^ {2} \cdot 8940} \approx 2.23 \, m$$

1 meter ≈ 3.28 feet

so $h \approx 2.23 \, \text{m}$ or $h \approx 2.23 \cdot 3.28 \approx 7.31$ feet.

Thus of 1 kg of copper we can get a wire length of 7.31 feet.

Copper based alloy ingots weighed approximately 20 pounds (9.1 kg)// http://en.wikipedia.org/wiki/Ingot

Also if you have one copper of ingot you can get a wire length of 66.52 feet (7.31·9.1 ≈ 66.52 feet).