Question

Assume that an average cell has a diameter of

5
5 micrometers ​(
5 times 10 Superscript negative 6
5×10−6 ​meter), which means it has a volume of
50
50 cubic micrometers. How many cells are there in a cubic​ centimeter?

Answer 1

Given that the volume of a cell is 50 cubic micrometers. It says to find the number of cells present in 1 cubic centimeter.

So we need to first convert the units of volume of a cell, then we can find the total number of cells in 1 cubic centimeter.

We know 1 meter = 100 centimeters = 1000000 micrometers

So 1 centimeter = 10000 micrometers

Taking Cubic powers on both sides :-

1 cubic centimeters = 10¹² cubic micrometers

1 cubic micrometers = 10⁻¹² cubic centimeters

50 cubic micrometers = 50 × 10⁻¹² = 5 × 10⁻¹¹ cubic centimeters

So volume of one cell = 5 × 10⁻¹¹ cubic centimeters

Number of cells =
`(Total\;\; volume)/(Volume\;\; of\;\; one\;\; cell) = (1\;cm^(3))/(5 * 10^(-11)\;cm^(3)) = (10^(11))/(5)` = 2 × 10¹⁰ cells.

So, total number of cells = 2 × 10¹⁰ cells.