Extremely hard mathmatical question?

Question

What is the area in square meters of 332 g Al foil that has a thickness of 21500 nm? The density of Al is 2.70 g/cm^3.

Answer 1

Ha, that's such a question :-)

A = 21,500nm = 21,500,000,000,000m = 2,150,000,000,000,000cm

B = 332g

content = A : B

content = 6,475,903,614,457.83g/cm3

With the density 2.7g/cm3, so content : density

=> 6,475,903,614,457.83 : 2.7

=> 23,984,828,202m2

I hv tried 2 ways but ended up same result...anyway, hope it helps.

Answer 2

density = mass / volume, so volume = mass / density

332 g / (2.70 g/ cm^3) = 122.96 cm^3

you know the thickness is 21500 nm

volume / thickness = area (in common units)...

Answer 3

A few equations that you should probably get familiar with.

volume = (area) x (thickness)

area = volume/thickness

denisty = mass/volume

volume = mass/density

You know density and mass, right?

And the thickness?

Need I say more?

Perhaps one more thing. Remember that units should be compatible. I mean you have a thickness in nm (I believe this is nanometer or 10^-9 meters) and a density using cm^3. You must convert one to the other before you can use them in the same calculation.

Answer 4

There are two steps to the problem:

1) Find out how much foil you have in cm^3

2) Find out the area of it if the thickness is 21500 nm

For part 1, divide 332 g by 2.70 g/cm^3.  This gives you the volume of foil.

For part 2, take the answer from part 1 and divide by 21500 nm (there is a units conversion to do) to get the area.  convert the area to m^2

Answer 5

Find the VOLUME of aluminum in 332 g.  You know the density.   It is about 120 cm^3.

Now the tricky part, the area = volume/thickness.

Make sure you have everything in consistent units.  

For example you can use 120cm^3 for volume, but your thickness becomes 2.15x10^4 nm x 10^-7 cm/nm

and 10^4 cm^2= 1 m^2

Answer 6

I will try to explain most of the steps...

Remember that volume=mass/density (V=M/D) and V=L*W*H and of course Area=L*W. You can now rearrange the formulas to make A*H=M/D then againto A=M/(D*H). You can now plug in the numbers.

Area=332g/(21500nm*2.70g/cm^3)

Converting nm to cm (10^9 to 10^2 which is 7 decimal places)

Area=332g/(0.00215cm*2.70g/cm^3)

cm and cm^3 cancel to make cm^2.

Area=57192 g/cm^2 (now convert to m^2 which is going to be move four decimal places left instead of two because it is squared)

Area=5.72m^2 -->Final Answer with Sig Figs too :)

Hope that helps!

Answer 7

If we've got 332g that means we've got 332/2.7 cm^3 of foil. That is 122.96cm^3 and 0.00012296m^3.

If the volume of this foil is v=l*w*h (lenght, width, height) and we have height(21500nm=0.000021500m) and volume(122.96m^3) we can calculate the area a=l*w.

l*w=a=v/h=0.00012296/0.0000215=5.72m^2

Answer 8

The volume of the sample is V = A*t where A is the area and t is the thickness. The density (D) is the mass (M) divided by volume (V). Therefore, the Area will be D/(M*t). Now, just be consistent with units.   Convert 21500 nm (10^-9m) into meters = (2.15 * 10^-5 m). The density is 2.70 g/cm^3 which is 2.7 * 10^6 g / m^3. That's because you convert 3 cm factors to m, each contributing a multiplying factor of 100 (10^2). Then just plug in to D/(M*t).