Question

Sabiendo que cada persona unos 4 500 000 glóbulos rojos por milímetro cúbico y que su cantidad de sangre es de 5 litros A) Que longitud ocuparían esos glóbulos rojos puestos en fila si su diámetro es de 0,008 milímetros por término medio? Expresalo en kilómetros B) Una vacuna tiene 100 000 000 bacterias por centímetro cúbico ¿ Cuantas bacterias habrá en una caja de 80 milímetros cúbicos cada una ?

Answer 1

Part A) distance covered by the aligned red cells is: 180000 Km

Part B) 8000000 bacteria (8 million bacteria)

Explanation:

Part A)

Let's first find the total number of red cells that the person has in the 5 liters, knowing that there are 4,500,000 of them in a cubic millimetre:

Since 1 liter contains 1,000,000 cubic millimetres, then, in 5 liters there must be 5 times that number of cubic millimetres. That is a total of 5,000,000 cubic millimetres.

Since in each cubic millimetre there are 4,500,000 red cells, then the number of red cells in the 5 liters must be the product of these two quantities:

4,500,000 x 5,000,000 = 22,500,000,000,000 red blood cells.

Now, to find the distance they will cover aligned one after the other, knowing that their average diameter is 0.008 mm is:

22,500,000,000,000 x 0.008 mm= 180000000000 mm

`22.5\,\,10^(12) * 8\,\,10^(-3)=1.8\,\,10^(11)` mm

In order to convert this distance into Km as requested, we use the fact that 1 mm = 0.000001 Km, or using exponents in base ten:

1 mm =
`10^(-6)\,\,Km`

Then, the distance covered in kilometers is:

`1.8\,\,10^(11)\,*\,10^(-6) \,\,Km=1.8\,\,10^(5)\,\,Km=180000\,\,Km`

Part B)

The vaccine contains a total of
`10^8` bacteria per
`cm^3`

In order to find how many bacteria we have in 80
`mm^3` of the vaccine, we first need to convert 80
`mm^3` into
`cm^3`:

`80\,\, mm^3 = 0.08 \,\,cm^3`

Then, if in one
`cm^3` there is
`10^8` bacteria, in
`0.08\,\,cm^3` there would be:
`0.08\,*\,10^8` bacteria. That is:
`8\,\,10^6` bacteria = 8000000 bacteria (eight million bacteria)