[IImaybelleII]

Copper has a density of 8.96 g/cm3. An ingot of copper with a mass of 57k (126 lbs) is drawn into a wire with a diamter of 9.50mm. What lenght of wire (in meters) can be produced? { Volume of wire= 3.14x radius squared x lenght}


 

At first i tried to figure out the volume using v= m/d I came out with a volume of 6.36. But then i looked at the volume of wire equation and got lost... someone please explain this to me step by step so i can understand how the arrived answer came to be.

[Borek]

Wire is a cylinder. Check formula for cylinder volume, solve for length - and you are ready.

[IImaybelleII]

I know that the formula for solving volume for a cylinder is pi x radius squared x height.

How can I do that formula without knowing the height? So far i have 3.14 x 4.75 squared x 


 

[ifuller]

In this case the height and the length are the same thing.... and are what you are trying to solve for. You have found the volume of copper to be 6.36, you know pi, you know the radius (diameter divided by 2) and you need to solve for the length.
Note: You will need to convert the diameter to centimeters in order to correctly solve for the length.
SO....
6.36=3.14*radius in centimeters*length
Solve for length.
Hope this helps

[IImaybelleII]

ahhhhh...

6.36= pi x radius squared x density=

3.14 x .475 squared x 8.96g= 6.35 ?

Is this right?

[enahs]

No. Units units units!
Your given amount of Cu is in kg (which you did not note correct). You density is in g. Convert one to the other.

Always include units in every step so you do not make silly mistakes!

[IImaybelleII]

 

I understand the units now and the process of canceling out..but im still confused as how to solve for lenght.

[enahs]

You can not set anything = to 6.36


57kg * ( 1 cm³) = 6.36, which you are using, but what units is that? kg*cm³/g. Is that a unit of volume?
            8.96 g


Either convert the density to kg or the mass of the given in kg to g and use the density in g.

And then why did you multiply by density?

Volume of a cylinder = π*r²*l

Definition of density.
d=m/v
You know the density and the mass, so solve for volume (with correct units!)
v=m/d

So you now know the volume of the cylinder, plug that in.
m/d = π*r²*l -> l = (m/d)/π*r²