how is it that capillaries have the most surface area but the least volume?

[tdod]

how is it that capillaries have the most surface area but the least volume (compared to veins and arteries)? I have never been able to understand the basic geometry behind this.

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[Chrisz]

You can account this using little bit algebra. We can assume the shape of a pipe to be cylinder. The surface area of a pipe with a height h and radius r.
The surface area is actually equal to the area wrapping to form the pipe, so A=2pi*r*h Volume of the pipe V=pi*r^2*h
Surface area/Volume=A/V=2pi*r*h/(pi*r^2*h)=2/r
We have derived the ratio A/V=2/r
So, as radius increase, the ratio gets smaller. As the radius decreases, the ratio gets bigger.

 

[type12]

Let's assume two objects have the same volume for a second: 1 liter each. If you have a square/cube, you've got 4-8 sides making contact with the outside. Now, imagine a very intricate star that has so many point and each point has such a low volume. Collectively, however, they add to the same volume as the square/cube.