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

Question

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

anonymous · Answer

@paki @toxicsugar22 
Can either of you help?

anonymous · Answer

@sweetburger can you help?

anonymous · Answer

@abb0t can you help?

anonymous · Answer

@aaronq

aaronq · Answer

|dw:1441146852206:dw|

aaronq · Answer

|dw:1441146891331:dw|

aaronq · Answer

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 · Answer

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

anonymous · Answer

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

anonymous · Answer

@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 · Answer

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

aaronq · Answer

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

anonymous · Answer

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

aaronq · Answer

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

anonymous · Answer

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 · Answer

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 · Answer

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 · Answer

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

aaronq · Answer

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

anonymous · Answer

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

anonymous · Answer

so it would just be 179.79 m^2

aaronq · Answer

they're asking you for square meters

aaronq · Answer

yeah

anonymous · Answer

Ok thanks!

aaronq · Answer

ok cool, no problem