0.958 ounces of copper is drawn into a wire with a length of 4.0 ft. What is the diameter (in millimeters) of the
wire? (The density of copper is 8.96 g/cm3
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First, we need to convert the given weight of copper into grams. The conversion factor is 28.3495 grams per ounce, so 0.958 ounces of copper is equal to 0.958 * 28.3495 = 27.209181 grams of copper.
Next, we need to convert the given length of the wire into centimeters. The conversion factor is 30.48 centimeters per foot, so 4.0 feet is equal to 4.0 * 30.48 = 121.92 centimeters.
Now we can calculate the volume of the wire using the formula:
Volume (in cm^3) = Weight (in g) / Density (in g/cm^3)
Volume = 27.209181 / 8.96 = 3.0346 cm^3
The volume of a cylinder is given by the formula:
Volume (in cm^3) = π * r^2 * h
Where r is the radius of the wire and h is its length. Since we are looking for the diameter of the wire, we need to double the radius. So, the formula becomes:
Volume = π * (2r)^2 * h
Simplifying this equation, we get:
3.0346 = 4π * r^2 * h
Since we know the length of the wire is 121.92 cm, we can substitute this value into the equation:
3.0346 = 4π * r^2 * 121.92
Now we can solve for the radius:
r^2 = 3.0346 / (4π * 121.92)
r^2 ≈ 0.00243439774
r ≈ sqrt(0.00243439774)
r ≈ 0.0493 cm
Finally, to convert the radius from centimeters to millimeters, we multiply by 10:
0.0493 cm * 10 = 0.493 mm
Therefore, the diameter of the wire is approximately 0.493 millimeters.