Suppose that pure gold was to be made into a very long, thin wire for high-end stereo systems. (Gold is often used because it does not oxidize so it makes very good electrical contacts). If the gold wire was to have a radius of 0.01 cm, how long of a wire could you make from 111 g. of gold?
Convert 111 g to the volume of gold by dividing by the density. Then use
Wire length = Volume/(pi*r^2)
To find out how long of a wire can be made from 111 g of gold, we need to use the formula for the volume of a cylinder, which, in this case, represents the gold wire.
The formula for the volume of a cylinder is:
V = πr²h
Where:
V is the volume,
r is the radius, and
h is the height or length.
In this case, we want to find the length of the wire, so the formula can be rearranged to:
h = V / (πr²)
To solve this problem, we first need to calculate the volume of the gold wire.
The density of gold is approximately 19.32 g/cm³. Therefore, the mass can be converted to volume using the formula:
V = m / ρ
Where:
V is the volume,
m is the mass, and
ρ is the density.
Plugging in the values, we have:
V = 111 g / 19.32 g/cm³
Now, we can calculate the length of the wire by substituting the volume and the radius into the rearranged formula:
h = V / (πr²)
h = (111 g / 19.32 g/cm³) / (π * (0.01 cm)²)
By simplifying the equation, we can calculate the length:
h ≈ 182,728 cm
Therefore, approximately 182,728 centimeters of wire can be made from 111 grams of gold, assuming a radius of 0.01 cm.