# Simple Density Question

1. May 18, 2006

### maej26

This is simple, but I'm missing the last step. I've almost got the answer.

--The standard kilogram is a platinum-iridium cylinder 39.0 mm in height and 39.0 mm in diameter. What is the density of the material?

I know that the correct answer is 2.15 x 10^4 kg/m^3.

If someone could tell me how to get from my answer, 2.15 x 10^-5, TO 2.15 x 10^4 I would really appreciate it. Thanks.

2. May 18, 2006

### dav2008

What are the units of the answer that you obtained? What are the units of the given answer?

That's the first thing you should always check when you obtain an answer that isn't consistant with a given answer.

3. May 18, 2006

### maej26

I know that's the problem but I just don't know how to do it and would really like to understand it seeing as how it's so basic.

4. May 18, 2006

### dav2008

Well the units of the given answer are kg/m3.

What are the units of the answer that you obtained?

5. May 18, 2006

### maej26

See, that's what I'm bad at.

I think it's kg/m^3 because (19.5 m)^2 makes it m^2 and that's multiplied by (39.0 m) therefore making it m^3. I'm not too sure though.

6. May 18, 2006

### dav2008

Right.

So if the desired units are kg/m3 and you used mm instead of m to solve for the density, what units could you use to obtain kg/m3 in your final answer?

Basically I'm saying that if you understand why your answer is in kg/mm3 then you should see what you could do to obtain an answer in kg/m3

7. May 18, 2006

### maej26

Okay, I just confused myself.

I guess what the more important question is if I didn't already know the correct answer how would I know that the units are supposed to be kg/m^3?

8. May 18, 2006

### dav2008

You don't, however typically you want your answers to be in standard mks units (everything in terms of meters, kilograms, seconds).

It's like asking if an answer of 1 hour is more correct than an answer of 60 minutes. They're equivalent.

9. May 18, 2006

### maej26

lol

(1000^3) (2.15 x10^-5)

10. May 18, 2006

### maej26

Okay, I get it now! Thanks! So, I basically had the correct answer all along. lol Do you think it would be marked correctly on an exam?

11. May 18, 2006

### dav2008

That's one way to do it. Since there are 10003 mm3 in 1 m3 you could multiply your answer that's in terms of kg/mm3 by 10003 to obtain an answer in terms of kg/m3

$$\frac{2.15\cdot10^{-5} \ kg}{1 \ mm^3} \cdot \frac{1000^3 \ mm}{1 \ m^3}=\frac{2.15 \cdot 10^4 \ kg}{m^3}$$

Another way to have done it is to just use meters instead of millimeters in your initial calculations.

$$\frac{1 \ kg}{(\pi){(.0195 \ m)}^2(.039 \ m)}=2.15 \cdot 10^4 \frac{kg}{m^3}$$

Last edited: May 18, 2006
12. May 18, 2006

### maej26

I think I like the latter better. I think I'll try that. Thanks! :)

13. May 18, 2006

### dav2008

It depends. Like I said usually answers are wanted in mks units unless otherwise specified. It can't hurt to ask your teacher/prof if they want certain units used.

14. May 18, 2006

### maej26

Okay, I'll keep that in mind.