Need help, please.
A copper wire (density = 8.96 g/cm^3) has a diameter of 0.25 mm. If a sample of this copper wire has a mass of 22 g, how long is the wire?
Thank you.
diameter = .025 cm
area = pi D^2/4= 4.91 * 10^-4 cm^2
so
4.91*10^-4 * L * 8.96 = 22
L = 5002 cm
or L = 50 meters
To find the length of the copper wire, you can use the formula for calculating the volume of a cylinder:
Volume = π * r^2 * h
where:
- π is a mathematical constant approximately equal to 3.14159
- r is the radius of the wire (which is half the diameter)
- h is the height or length of the wire
First, let's calculate the radius of the wire. The diameter is given as 0.25 mm, so to find the radius:
Radius = diameter / 2 = 0.25 mm / 2 = 0.125 mm
Next, we need to convert the radius to centimeters as the density is given in g/cm^3. There are 10 mm in 1 cm, so:
Radius = 0.125 mm * (1 cm / 10 mm) = 0.0125 cm
Now, we can calculate the volume of the wire using the formula. The mass of the wire is given as 22 g, and the density is given as 8.96 g/cm^3. The density can also be expressed as mass per unit volume:
Density = mass / volume
Solving for volume:
Volume = mass / density = 22 g / 8.96 g/cm^3 = 2.4553571 cm^3
Now, we have the volume of the wire, and we can solve for the length. Rearranging the formula for volume:
Volume = π * r^2 * h
h = Volume / (π * r^2)
Substituting the values:
h = 2.4553571 cm^3 / (3.14159 * (0.0125 cm)^2)
Calculating the length:
h = 198.089674 cm
Therefore, the length of the copper wire is approximately 198.09 cm.