Question

The density of water is about 1 gram per milliliter. A milliliter is a cubic centimeter (i.e., cm3 ). A red blood cell has a density similar to water and is shaped like a one micrometer thick disk with a diameter of about 10 micrometers. About what is the mass in grams of a red blood

Answer 1

The mass in grams of a red blood cell is about 7.85 × 10⁻¹¹ grams

Step-by-step explanation:

To find the mass in grams of a red blood cell,

From,

`Density = (Mass)/(Volume)`

Then,

`Mass = Density * Volume`

From the question,

Density of a red blood cell is similar to that of water

Density of water = 1 g/mL = 1 g/ cm³

Then, Density of a red blood cell = 1 g/cm³

Now, we will find the volume a red blood cell.

From the question,

• A red blood cell is shaped like a one micrometer thick disk with a diameter of about 10 micrometers

Since the shape is like that of a thick disc, we can determine the volume by using the formula for volume of a cylinder.

Hence,

Volume of a red blood cell =
`\pi r^(2)h`

Where
`\pi` Is a constant (Take
`\pi` = 3.14)

`r` is the radius

and
`h` is the thickness

Diameter of a red blood cell = 10 micrometers

Then, radius of a red blood cell = 10/2 micrometers = 5 micrometers

`r` = 5 micrometers = 5 × 10⁻⁶ meters

and
`h` = 1 micrometer = 1 × 10⁻⁶ meters

Hence,

Volume of a red blood cell = 3.14 × (5 × 10⁻⁶)² × 1 × 10⁻⁶

∴ Volume of a red blood cell = 7.85 × 10⁻¹⁷ cubic meter (m³)

Convert this to cubic centimeter

(NOTE: 1 cubic meter = 1000000 cubic centimeter)

Hence,

Volume of a red blood cell = 7.85 × 10⁻¹¹ cubic centimeter (cm³)

Now, for the mass

`Mass = Density * Volume`

Density of a red blood cell = 1 g/cm³

Volume of a red blood cell = 7.85 × 10⁻¹¹ cubic centimeter (cm³)

Then,

Mass = 1 g/cm³ × 7.85 × 10⁻¹¹ cm³

Mass = 7.85 × 10⁻¹¹ g

Hence, the mass in grams of a red blood cell is about 7.85 × 10⁻¹¹ grams