Assume that an average cell has a diameter of 7 micrometers (7x 10(6) meter), which means it has a volume of 200 cubic micrometers. How many cells are there in a cubic centimeter?
+9465 We want to know... how many cells are there in a cubic centimeter?
That is.....how many 200 cubic micrometers are there in a cubic centimeter?
We want to know...what is \(\frac{1\,\text{ cubic centimeter}}{200\,\text{ cubic micrometers}}\) ?
First let's convert 200 cubic micrometers into cubic centimeters.
1 meter = 1 · 102 centimeters = 1 · 106 micrometers
| 1 · 102 cm | = | 1 · 106 µm | Divide both sides by 106 . | |
| 1 · 102 / 106 cm | = | 1 µm | ||
| 1 · 10-4 cm | = | 1 µm | Cube both sides. | |
| (1 · 10-4 cm)3 | = | (1 µm)3 | ||
| 1 · 10-12 cm3 | = | 1 µm3 | Multiply both sides by 200 . | |
| 200 · 10-12 cm3 | = | 200 µm3 | ||
| 2 · 10-10 cm3 | = | 200 µm3 |
So.....
\(\frac{1\,\text{ cubic centimeter}}{200\,\text{ cubic micrometers}}\,=\,\frac{1\,\text{ cubic centimeter}}{2 \cdot 10^{-10}\,\text{ cubic centimeters}}\,=\,\frac{1}{2\cdot10^{-10}}\,=\,5\cdot10^9\)
