Ok, my mom called me asking for my help (she thinks I'm some kind of math wiz, though I've told her over and over that I'M NOT lol) on a math problem. Here it is:

An average capillary is 8 micrometers in diamater. What length capillary, in meters, is required to contain 1 cubic centimeterof blood?

She gave me a conversions and a formula.

1ml = 1 cc = 1 cubic centimeter

volume (of a cylinder) = (length)(pi)(radius^2)

I filled in formula this way:

1 cm^3 = (length)(pi)(16micrometers).

Converted, 16 micrometers centimeters = 1.6 cm (if 1micrometer is 1/1000th of a meter and 1 cm is 1/100th).

formula: 1cm^3 = (length)(pi)(1.6cm)

Now, I know she can divide by pi using her calculator, so I think we have all the necessary numbers...my only problem is: how do you divide a volume by a length?! Because a cubic centimeter is a volume and 1.6 cm is a length and I'm not sure how to figure that out. She is calling someone else for help, but it is bugging the CRAP out of me >_<

Anyone?

*blinks*

I'm so sorry... You lost me at 1ml = 1 cc = 1 cubic centimeter.

Wish I could help but math isn't my strongest suit, especially now that I have been out of school for two years. Hope someone else is able to help.

You just divide it. Ignore the units, because they work themselves out.

For instance, the area of a rectangle is length x breadth. If you knew the area was 20cm^2 and the length was 5cm, you'd still divide the area by the length to get the breadth of 4cm. In fact, the area has to be in cm^2 because you're not just multiplying the numbers, but the units too.

With a volume, it is a length times a length (that is a length squared) times a length. So of course the volume has different units from the parts that multiply together to get it. But that doesn't affect what you do with the numbers.

Except - are you sure about micrometers? I thought they were smaller than that. And I googled and saw this: 1 centimetre = 10 000 micrometres

Well, she said that that is what micrometers were. My internet isn't fast enough to work with google most of the time, so I didn't get to look it up myself lol.

Part of the problem is that your formula is pi times the radius squared. 8 squared is 64, not 16.

8 is the diameter, so 4 is the radius.

Daaaamn, iWRITE pwning some ass on math terms.

LOL. Not at all. Just makin' sure we're all on the same page ;)

Doh! That's what I get for reading it fast. Never mind! lol

Wouldn't it be .01 meters? Because 1 cubic centimeter = 10,000 micrometers & 10,000 micrometers = .01 meters

Okay, here's how I did it:

volume of a cylinder:

Volume = pi x r^2 x length

Volume = 10,000 cubic micrometres

r = 4 micrometres

length = unknown

So,

10,000 = pi x 4^2 x length

rearranged,

length = 10,000 / (16 x pi)

which gives a lengh of approx 199 micrometres

in METRES, that's 199 (micrometres) / 1000 (to get to mm) / 1000 (to get to m) = 0.000199 m

And in answer to your question, you're dividing the volume by pi and the radius squared to GET the length. It's all to do with rearranging the equation. As Estella said, the units work themselves out. =)

Okay so ignore my previous post, lol. I made a BIG mistake. xD Forgot to cube things.

The volume is not 1cm cubed = 10,000 micrometres cubed, but 1,000,000,000,000 (so 12 zeros!!!)

So length = 10^12 / (16 x pi)

which gives a length of 19,994,368,226 micrometres

OR 19,994 metres.

That's a lot of metres. xD

oohhh, yes. That makes sense. I was doing it the hard way and dividing the volume first by 16 then by pi and then trying to convert to cm^3 instead of converting to micrometers first and just doing it the easy way, hah.

Yeah, I came up with a number similar to that (but definitely wrong) and my first thought was: "No, that's wrong. 20,000 meters of vein in my body only carries 1cc of blood? I just donated plasma last week and they took out 10 times that much! lol but then she told me capillaries aren't your regular veins. So that made more sense.

And thanks!

Apparently, 19, 994 was wrong. She ended up with that answer anyway and..it was wrong. lol.

lol! Ahhh well, I tried. xD

haha yea, that's all we can ask. apparently it was some reaaaalllyyy small number. lol. if we convert everything to meters first, it may be easier. But I'm with @Lauren. - My brain hurts too much to attempt it right now..lol

My brain. It aches.