- anonymous

How would you get d= 7300 m^3 to m^2?
An electrolytic tin-plating process gives a coating of 3.0 x10^-5 inches thick. How many square metres can be coated with 1kg of tin, d=7300 kg/m^3...is the full question, please just help me get the m^3 to m^2

- schrodinger

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- anonymous

@paki @toxicsugar22
Can either of you help?

- anonymous

@sweetburger can you help?

- anonymous

@abb0t can you help?

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## More answers

- anonymous

- aaronq

|dw:1441146852206:dw|

- aaronq

|dw:1441146891331:dw|

- aaronq

I meant 0.00003 inches for height, which is 7.62e-7 m (conversion done by google cuz i'm not 'murican).
This is a volume, not a surface, but it has a fixed height.
\(V=l*w*h=l*w*(7.62*10^{-7}~m)\)
The volume of tin must be found with the mass and the density.
\(\rho=\dfrac{m}{V}\rightarrow V=\dfrac{m}{\rho}=\dfrac{1~kg}{7300~kg/m^3}=0.0001369863013699~m~\approx0.000137~m^3\)
\(V=l*w*(7.62*10^{-7}~m)= 0.000137~m^3\)
Well make this a square base, so: \(x^2*(7.62*10^{-7}~m)= 0.000137~m^3\)
Finally we solve for x and we get one of the sides of our coating.|dw:1441147497222:dw|

- aaronq

Actually solving for \(x^2\) gives you the area of the coating, so yeah you can stop there

- anonymous

will solving for x^3 give us a m^2 answer?

- anonymous

@aaronq ok, so looking at this, firstly thank you, but why are we finding volume, instead of let's say area? Is it because the coating has a thickness?

- aaronq

yes, the thickness indicates that the object has 3 dimensions and has a volume.
Solving for \(\sf x^2\) gives you the area

- aaronq

The thickness indicates how large the material can coat the area. A thinner coating will give a larger area and viceversa.

- anonymous

Awesome Thanks, @aaronq
I got 13.41m^2
Is this correct?!?

- aaronq

no problem!
sorry, idk my calculator is elsewhere.
just divide the volume by the height and that should be it

- anonymous

Ok... I did 1.37*10^-4 (volume) / 7.62*10^-7 (height) = 179.79m^4
Then finally took the square root of that and got 13.41m^2

- anonymous

But, i don't know if that is how the exponents on metres goes???
Sorry to keep asking things, just want to make sure i'm absolutely correct on units (my teacher is strict on units)
@aaronq

- aaronq

the will cancel out and give you \(m^2\), remember i told you to follow the formula and divide the volume by the height?
\(\sf \dfrac{volume}{height}=\dfrac{m^3}{m}=m^2\)

- anonymous

ok but then do you just leave the x^2???

- aaronq

So you have \(x^2*(7.62*10^{-7}~m)= 0.000137~m^3\)
then just isolate \(x^2\)

- anonymous

because if you take the square root of 179.79 m^2 it comes out 13.41 m

- anonymous

so it would just be 179.79 m^2

- aaronq

they're asking you for square meters

- aaronq

yeah

- anonymous

Ok thanks!

- aaronq

ok cool, no problem

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