# I thought conversions were simple

I thought conversions were simple, but this one is giving me some trouble. If anyone could help out, it would be greatly appreciated. Thanks in advance.

http://img225.imageshack.us/img225/6229/pjhyscb0.png [Broken]

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hage567
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If there are 50 water drops of radius 10 um, what total volume is that?

im confused to find volume with only radius..:(

hage567
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What's the volume of a sphere? (The radius is the only thing you need to know)

4.18879x10^-10 in meters

hage567
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It's r^3, I think you may have done r^2. The units would be m^3 since it's volume, right?

$$V = \frac{4 \pi r^3}{3}$$

sorry, yeah ^3 i did squared. so.. 4.18879x10^-15

hage567
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OK, so what's the volume of a cylinder of height 2.9 km and radius 1.4 km?

The way to approach this problem is to find out how many cubic centimeters there are in the whole cloud. Once you have that, you can figure out how much water there is in the entire cloud because you now know how much there is in one cubic centimeter.

hage567
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sorry, yeah ^3 i did squared. so.. 4.18879x10^-15
Remember to write down your units. That's the whole point of this problem and you will make mistakes if you lose track of them.

So this should be in m^3.

Don't forget to multiply this by 50 to get the total volume of the 50 drops in the cubic centimeter of cloud.

in the cylinder, volume is 1.7856x10^10 m^3, right?

hage567
Homework Helper
in the cylinder, volume is 1.7856x10^10 m^3, right?
Yes, that's right.

Remember to write down your units. That's the whole point of this problem and you will make mistakes if you lose track of them.

So this should be in m^3.

Don't forget to multiply this by 50 to get the total volume of the 50 drops in the cubic centimeter of cloud.
after x by 50 the answer is 2.0949x10^-15. what do i do with the cylinder now?

hage567
Homework Helper
So if there is 2.09x10^-15 m^3 of water for every cm^3 of cloud, how much water is there is 1 m^3 of cloud? (Just convert cm^3 to m^3)

Then, you can find out how much water is in the entire cloud by multiplying by the entire volume of the cloud you just found.

2.09x10^-12 per m^3. so now this times 1.7856x10^10 m^3?

hage567
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2.09x10^-12 per m^3. so now this times 1.7856x10^10 m^3?
1 m^3 = 100^3 cm^3. You must cube the 100.

So it should look like $$\frac{2.09x10^-15 m^3 water}{1 cm^3 cloud} * \frac{100^3 cm^3}{1 m^3}$$

Does that make sense?

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yeah that looks good, i forgot about the cubing of the 100. and now same for the 500 correct? but also. thats not the final is it

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hage567
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Yes. What answer did you get?

2.09x10^-9 is what i got for the 50. now i will do it for the 500. any idea for part b and or c?

hage567
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2.09x10^-9 is what i got for the 50. now i will do it for the 500. any idea for part b and or c?
Don't forget to multiply by the entire volume of the cloud.

For (b) How many m^3 in a Liter?

For (c), what's density?

Give these a try and see what you can do.

3.7319x10^1 correct for 50?

B) .00 m^3
c) p= m/v

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hage567
Homework Helper
2.09x10^-9 i thought that was the asnwer after multiplying the vol of cloud.
No, the 2.09x10^-9 m^3 is the volume of water per m^3 of cloud. To find the total volume of water you must multiply by the total volume of the cloud.

B) .00 m^3 c) p= m/v
Yes. So how might you use that to figure out the mass of water in the cloud?

hage567
Homework Helper
3.7319x10^1 correct for 50?
OK, that looks better (watch your sig figs). Don't forget to state your units! It's a good habit to get into.

OK, that looks better (watch your sig figs). Don't forget to state your units! It's a good habit to get into.
but is correct answer right? only 1 try on this homework problem :(.

.001 i meant to say sorry.

use mass of cloud divided by the volume we just found?

A) is correct thanks

B) .001 m^ = 1 L?

C) just use density formula?

hage567
Homework Helper
B) .001 m^ = 1 L?
Yes. (m^3)

C) just use density formula?
Yes, you know the volume now and you were given the density.