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?
Why did the copper wire go on a diet? It wanted to watch its mass!
But seriously, let's calculate how long the wire is. We can start by finding the volume of the wire using its mass and density. The formula to find the volume is:
Volume = Mass / Density
Plugging in the values, we get:
Volume = 22 g / 8.96 g/cm^3
Now, we need to find the cross-sectional area of the wire to calculate the length. The formula for the area of a circle is:
Area = π * (radius)^2
The diameter of the wire is 0.25 mm, which means the radius is half of that (0.25 mm / 2 = 0.125 mm). However, it's more convenient to use centimeters, so let's convert the radius to cm:
Radius = 0.125 mm = 0.125 cm
Now, let's calculate the area:
Area = π * (0.125 cm)^2
Finally, we can find the length of the wire by dividing the volume by the cross-sectional area:
Length = Volume / Area
Go ahead and plug in the numbers to get the final answer. I hope this wire turns out to be longer than a bad joke!
To find the length of the copper wire, we can use the formula:
Volume = Mass / Density
The volume of a cylinder is given by:
Volume = π * radius^2 * height
In this case, the radius is half of the diameter, so:
radius = 0.25 mm / 2 = 0.125 mm = 0.0125 cm
Substituting the radius into the volume formula, we get:
Volume = π * (0.0125 cm)^2 * height
Now, rearranging the formula for Volume and substituting the given mass and density, we can solve for the height (length) of the wire:
Mass / Density = π * (0.0125 cm)^2 * height
height = Mass / (π * (0.0125 cm)^2 * Density)
Plugging in the values:
height = 22 g / (π * (0.0125 cm)^2 * 8.96 g/cm^3)
Calculating the height, we find:
height ≈ 22 g / (π * 0.00015625 cm^2 * 8.96 g/cm^3)
height ≈ 24447.55 cm
Therefore, the length of the copper wire is approximately 24447.55 cm.
To find the length of the wire, we can use the formula for the volume of a cylinder:
Volume = π * (radius^2) * height
The radius of the wire can be found by dividing its diameter by 2:
radius = diameter / 2
Given that the diameter is 0.25 mm, the radius would be:
radius = 0.25 mm / 2 = 0.125 mm
Now, we need to convert the radius to cm since the density is given in g/cm^3. There are 10 mm in 1 cm, so:
radius = 0.125 mm / 10 = 0.0125 cm
The mass of the wire is given as 22 g, and we know that the density is 8.96 g/cm^3. Density is defined as mass divided by volume:
density = mass / volume
Rearranging the formula, we can solve for volume:
volume = mass / density
Substituting the values:
volume = 22 g / 8.96 g/cm^3
volume ≈ 2.4554 cm^3
Using the formula for the volume of a cylinder, we can find the height (length) of the wire:
volume = π * (radius^2) * height
Rearranging the formula, we can solve for height (length):
height = volume / (π * (radius^2))
Substituting the values:
height = 2.4554 cm^3 / (π * (0.0125 cm)^2)
height ≈ 16.73 cm
Therefore, the length of the copper wire is approximately 16.73 cm.
0.25 mm * 1 cm/10 mm = 0.025 cm
so
r = 0.0125 cm
Area = pi r^2 = 4.91*10^-4 cm^2
volume = Area * x = 4.91*10^-4 x cm^3
so
8.96 g/cm^3* 4.91*10^-4 x cm^3 = 22 g
x = 5002 cm
= 50 meters