Respuesta :
Answer:
The length of the wire = 352.66 feet.
Explanation:
A copper refinery produces a copper ingot weighing 150 lb. If the copper is drawn into wire whose diameter is 9.50 mm, 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 the radius and h is its height or length.)
Step 1: Convert lb to kg
150 lb = 68.0389 kg
Step 2: Calculate volume of copper
Volume = mass / density
Volume = 68038.9 grams / 8.94 g/cm³
Volume = 7610.6 cm³ Cu
Step 3: Calculate length of wire
The diameter of the wire is 9.50 mm, so the radius is half of that (4.75 mm), or 0.475 cm.
The total "volume" of the wire is πr²h = (π)*(0.475 cm)²(h) = 0.708h = 7610 cm^3
7610 = 0.708h
h = 10749 cm = length of wire
The length of the wire = 352.66 feet.
The length of the wire is 2369.84cm
Data Given;
- density = 8.94 g/cm^3
- diameter = 9.50mm = 0.95cm
- radius = d / 2 = 0.95/2 = 0.475cm
- mass (not given, but assuming m = 15kg = 15000kg
Density of the Wire
Let's calculate the volume of the wire using formula of density.
[tex]density = \frac{mass}{volume}\\[/tex]
substitute the values and solve for volume
[tex]density = mass/ volume\\volume = mass / density \\volume = 15000/ 8.94\\volume = 1677.85cm^3[/tex]
Length of the Wire
To calculate the length of the wire, we would use the volume of a cylinder on this.
[tex]v = \pi r^2h\\1677.85 = 3.14 * 0.475^2 * h\\1677.85=0.708h\\h = 2369.84cm[/tex]
From the calculation above, the length of the copper is 2369.84cm
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