# Homework Help: Unit conversion with density of gold

1. Jan 16, 2014

### jdawg

1. The problem statement, all variables and given/known data
Gold, which has a density of 19.32 g/cm3, is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber. (a) If a sample of gold with a mass of 4.713 g, is pressed into a leaf of 6.549 μm thickness, what is the area of the leaf? (b) If, instead, the gold is drawn out into a cylindrical fiber of radius 2.400 μm, what is the length of the fiber?

2. Relevant equations

d=m/v, V=(l)(w)(h)
V=pi(r^2)h
3. The attempt at a solution
Part A.] First I found the volume by dividing 4.713g by 19.32g to get 0.2439cm^3.
Then I converted 6.549μm to cm: (6.549μm)(1cm/10000μm)=6.549cm
Then I solved for area by dividing (0.2439cm^3) by (6.549E-4) and got 372.49cm^2
Then I converted 372.49cm^2 to m^2 by dividing by 100 and got 3.72m^2 for the area.(But my online homework said this was wrong)
Part B.]I converted the radius 2.400μm to 2.4E-4cm, squared 2.4E-4cm, then multiplied by pi, and divided the volume from part A (0.2439cm^3), and solved for the height and got 1327843.425cm and converted to 13478.43m , which seems really wrong...

Please help, I can't figure out what I'm doing wrong.

2. Jan 16, 2014

### nasu

How many cm^2 in a m^2?

3. Jan 16, 2014

### SteamKing

Staff Emeritus
Part B. How do you go from 1327843.425 cm to 13478.43 m? How many cm in 1 m?

4. Jan 16, 2014

### jdawg

Is it 100?

5. Jan 16, 2014

### jdawg

@SteamKing I just divided 1327843.425 by 100

6. Jan 16, 2014

### nasu

If you mean 1m^2 = 100 cm^2 then no.
If 1m=100 cm, then
1m^2=1mx1m= ?

7. Jan 16, 2014

### jdawg

10000?

8. Jan 16, 2014

### jdawg

Thanks guys! I fixed part A. I didn't think about having to square 100.

9. Jan 16, 2014

### SteamKing

Staff Emeritus
If that's what you did, then your answer of 13478.43 got scrambled somehow.
After all, dividing 1327843.425 means moving the decimal point two spaces to the left.

Always check your work to avoid silly mistakes.

10. Jan 16, 2014

### jdawg

Oh sorry, I think I just typed it wrong. But when I entered 13278.4325 as an answer it was still wrong, so what did I do wrong in part B?

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