Unit conversion with density of gold

[jdawg]

Homework Statement

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?

Homework Equations

d=m/v, V=(l)(w)(h)
V=pi(r^2)h

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.

 

[nasu]

How many cm^2 in a m^2?

 

[SteamKing]

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

 

[jdawg]

Is it 100?

 

[jdawg]

@SteamKing I just divided 1327843.425 by 100

 

[nasu]

Is it 100?

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

 

[jdawg]

10000?

 

[jdawg]

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

 

[SteamKing]

@SteamKing I just divided 1327843.425 by 100

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.

 

[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?