Answer:
118,900,000,000,000 (1.189 × 10^14)
Step-by-step explanation:
First, assume that a cell is roughly a sphere with radius 10−³cm (. Let's compute the volume of the cell from the relation between radius and volume:
The volume V of a sphere with radius r is
V=(4π)/3 r³
where r³ and V have the same units. The volume of a cell with radius 10−³cm is therefore
V=4π³/3(10−³)3≈4.1888×10−⁹ cm³.
Next, we use the fact that the density of a cell is approximately the density of water which is 1g/cm³. Let's compute the mass of a cell from its volume and density using the definition of density:
density = mass/volume
which is equivalent to
mass = density×volume.
The mass of a cell is therefore
1 (g)/cm³×4.1888×10−⁹cm³ ≈ 4.1888×10−⁹g.
Now you know the mass of a cell, what other piece of information do you need to work out the number of cells in your body? Your mass in grams (if you know your weight in pounds, you can convert: 1 lb≈453.6 grams).
Number of cells=Your Mass/Mass of Cell
For example, the mass of a 175 lb is about 45,360 grams. We have that
79378g/4.1888×10−⁹g≈11.89 × 10^14
so there are approximately 1×10¹⁴=118,900,000,000,000 (1.189 × 10^14) cells in the human body!
