# Thread: Finding thickness given width, length, mass, density

1. ## Finding thickness given width, length, mass, density

Here's the problem:

A sheet of metal is 29.4 mm wide and 16.1 mm long. If it weighs 4.093 g and the density of the metal is 7.23 g/cm3, what is the thickness of the sheet (in mm)?

I'm not sure how I would begin to approach a problem like this as it's asking for a variable I'm not sure how to solve down for. Any help towards this problem will be more then appreciated, thank you.

2. Originally Posted by hemi
Here's the problem:

A sheet of metal is 29.4 mm wide and 16.1 mm long. If it weighs 4.093 g and the density of the metal is 7.23 g/cm3, what is the thickness of the sheet (in mm)?

I'm not sure how I would begin to approach a problem like this as it's asking for a variable I'm not sure how to solve down for. Any help towards this problem will be more then appreciated, thank you.
Density

$d=\frac{m}{V}$ by definition.

You've got $d=7.23g/cm^3$ and $m=4.093g$

Solve for $V$.

Then put

$V=(29.4mm)(16.1mm)t$ where $t=thickness$ in millimeters.

PS Remember to convert.

BTW: Posts:37, Thanks:0

3. Originally Posted by VonNemo19
Density

$d=\frac{m}{V}$ by definition.

You've got $d=7.23g/cm^3$ and $m=4.093g$

Solve for $V$.

Then put

$V=(29.4mm)(16.1mm)t$ where $t=thickness$ in millimeters.

PS Remember to convert.

BTW: Posts:37, Thanks:0
Thanks.

So I found $V=m/d$ and ended up getting the value $0.5661$. Now I'm a bit confused about this part:

$V=(29.4mm)(16.1mm)t$ where $t=thickness$ in millimeters.

What is this $t$ variable? Am I going to rearrange for $t$ by plugging in the $V$ value I have calculated?

Yeah I haven't been thanked much I guess. Don't really know what to say about that?

4. Originally Posted by hemi
What is this $t$ variable? Am I going to rearrange for $t$ by plugging in the $V$ value I have calculated?
Yes.

Originally Posted by hemi
Yeah I haven't been thanked much I guess. Don't really know what to say about that?
I was thinking in the opposite order.

5. So thus I can write:

$t = (29.4mm)(16.1mm)/0.5661$ and therefore $t = 836mm$ thick? Is this correct?

Also what is the unit on the value $0.5661$, cubic centimeters (cc)?

This answer doesn't seem logical to me. The sheet is thicker then its length and width?

6. Originally Posted by hemi
So thus I can write:

$t = (29.4mm)(16.1mm)/0.5661$ and therefore $t = 836mm$ thick? Is this correct?

Also what is the unit on the value $0.5661$, cubic centimeters (cc)?

This answer doesn't seem logical to me. The sheet is thicker then its length and width?
You have to convert density to mm before you begin.

7. Alright so let me try to rework it:

The Density Conversion:

$\frac{7.23g/cm^3}{10mm} = 0.723 g/mm^3$

The volume calculation:

$V = m/d$
$V = \frac{4.093g}{0.723 g/mm^3} = 5.66 mL$

The rearrangement:

$V = (29.4mm)(16.1mm)t$

$t = \frac{29.4mm)(16.1mm)}{5.66mL} = 83.62mm$

This still seems a bit strange to me. I feel like I'm doing something wrong.

8. Originally Posted by hemi
Alright so let me try to rework it:

The Density Conversion:

$\frac{7.23g/cm^3}{10mm} = 0.723 g/mm^3$

The volume calculation:

$V = m/d$
$V = \frac{4.093g}{0.723 g/mm^3} = 5.66 mL$

The rearrangement:

$V = (29.4mm)(16.1mm)t$

$t = \frac{29.4mm)(16.1mm)}{5.66mL} = 83.62mm$

This still seems a bit strange to me. I feel like I'm doing something wrong.
This rearangement that you speak of... Here it is:

$V=l\cdot{w}\cdot{t}$

Therefore

$t=\frac{V}{l\cdot{w}}$

You've got

$t=\frac{l\cdot{w}}{V}$

See my point?

And where is the mL coming from? We're talking about a solid, right?

9. Alright so right from the start:

The Density Conversion:

$\frac{7.23g/cm^3}{10mm} = 0.723 g/mm^3$

The volume calculation:

$V = m/d$
$V = \frac{4.093g}{0.723 g/mm^3} = 5.66 mL$

The rearrangement:

$V = (29.4mm)(16.1mm)t$

$t = \frac{5.66mm} {29.4mm)(16.1mm)} = 0.011957578mm$

That still doesn't seem correct to me?

Sincerely Von, thanks for your help and patience, I know it may seem quite obvious to you, this is relatively new stuff for me. So thanks a lot for everything.

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# how to calculate thickness with density

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