# A laboratory worker prepared a 1:200 dilution of whole blood. The diluted blood gave a count of 30 RBCs per hemocytometer square (100 µm × 100 µm). How many RBCs are in 1 mL of the diluted blood and in 1 mL of the whole blood?

Aug 22, 2017

There are "3,0" × 10^7 red blood cells in 1 mL of the diluted blood and "6,0" × 10^9 RBCs in 1 mL of whole blood.

#### Explanation:

Step 1. Calculate the volume of a hemocytomer square

V = lwh = 100 color(red)(cancel(color(black)("µm"))) × 100 color(red)(cancel(color(black)("µm"))) × "0,10" "mm" × ((1 "mm")/(1000 color(red)(cancel(color(black)("µm")))))^2

$= {\text{1,00" × 10^"-3" color(white)(l)"mm}}^{3}$

So, there are 30 RBCs in ${\text{1,00" × 10^"-3"color(white)(l) "mm}}^{3}$.

Step 2. Calculate the number of RBCs in a volume of ${\text{1 cm}}^{3}$ (1 mL)

$\text{RBCs" = 1 color(red)(cancel(color(black)("cm"^3))) × ((10 color(red)(cancel(color(black)("mm"))))/(1 color(red)(cancel(color(black)("cm")))))^3 × "30 RBCs"/("1,00" × 10^"-3" color(red)(cancel(color(black)("mm"^3)))) = "3,0" × 10^7color(white)(l) "RBCs}$

Step 3. Calculate the number of RBCs in 1 mL of whole blood

∴ In 1 mL of whole blood,

$\text{RBCs" = 200 × "3,0" × 10^7color(white)(l) "RBCs" = "6,0" × 10^9 color(white)(l)"RBCs}$