# #6 How many cells are there in human body?

(Hint: The inventor of the microscope used his first crude microscope with a magnification of 10 & 100)

Solution

For estimating the number of cells in the human body let’s approximate our body as a box of length L,W and H.

Since, we always want to deal with round numbers, let’s assume our length to be 6 feet.

Now, for the width, let’s average over our head, neck, torso, legs and feet. Let’s decide to take an average width of 1 feet.

As of H, let’s assume it to be about 6 inches (or ½ feet)

Our volume will simply be 6 * ½ * 1 = 3 cubic feet.

We know that 1 meter cube is 3 * 3 * 3 cubic feet (since 1 meter = 3 foot)

Or 1 meter cube will be 0.1 cubic meter.

Now, let’s figure out the size of a cell using our own eyes!

Of course, a human cell cannot be seen without an unaided eye. But, I can easily look at 1/10th of a milli meter (10^-4 meter) without any help. Using the hint, we know that the inventor of the microscope used his first crude microscope with a magnification of 10 & 100

So, a typical cell must be 10 to 100 times smaller than 10^-4 meter.Thus, the typical cell must be around 10^-5 to 10^-6 meter (or 1 to 10 micrometers). A typical cell with a diameter of 10 micrometer will have a volume of (10^-5)^3 = 10^15 cubic meter

Or, the number of cells in our body will just be the ratio of 10^-1 cubic meter / 10^-15 cubic meter (i.e the ratio of both the volumes)

Or, about 10^14 cubic meter. Or about 100 trillion cells exist in the human body!

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