# The Volume of a red blood cell is about 90.0 x 10^-12cm3 assuming that red blood cells are...

## Question:

The Volume of a red blood cell is about 90.0 x 10^-12cm3 assuming that red blood cells are sperical, what is the diameter of a red blood cell in millimeters.

## Volume of a Sphere

The formula for the volume of a sphere is given in terms of the diameter {eq}d {/eq} as

{eq}\displaystyle V = \frac{4}{3}\pi(\frac{d}{2})^3 {/eq}.

Into the equation for the volume of a sphere,, i.e.,

{eq}\displaystyle V = \frac{4}{3}\pi(\frac{d}{2})^3 {/eq}.

we can substitute for the volume of the red blood cell as

{eq}V = 90.0 \times 10^{-12} \ cm^3 {/eq}

and write:

{eq}\displaystyle 90 \times 10^{-12} \ cm^3 = \frac{4}{3}\pi\times \frac{d^3}{8} {/eq}.

Upon evaluating, we have:

{eq}d^3 = 1.71 \times 10^{-10} \ cm^3 {/eq}.

Taking the cube root, we obtain the diameter as:

{eq}d = 5.55 \times 10^{-4} \ cm {/eq}.

We are asked for this value in mm. We make use of the conversion factor {eq}1 \ cm = 10 \ mm {/eq}, thus obtaining,

{eq}d = 5.55 \times 10^{-4} \ cm \times 10 \ mm/cm = 5.55 \times 10^{-3} \ mm {/eq}.