A typical human cell is approximately 10 μm in diameter and enclosed by a membrane that is 4.4 nm thick. To simplify the calculations, model the cell as a sphere.

Question

1.What is the volume of the cell? I got this= 524.49, it is correct

2.What is the volume of the cell membrane? 

3.What percent of the cell volume does its membrane occupy?

I need help on the last two parts of the question

Answer 1

Anisha

As your small dimensions is nm, I would work in nm consistently.

1 nm = 1000 μm

So the diameter is 10μm = 10000 nm = 10⁴ nm. So radius = 0.5 x 10⁴ nm

So cell volume = 4/3 π r³ = 4/3 π (0.5 x 10⁴)³ nm³ = 5.236 x 10¹¹ nm³ (This is close to you answer, I used 3.1415927 for π)

For the second part : volume of membrane = volume of cell - volume of cell without the membrane

The volume of the cell we have already.

For the volume of the cell without the membrane - find the volume of a sphere radius : (0.5 x 10⁴) - 4.4 (so radius is 4995.6 nm).

(we subtract the 4.4 as it is the thickness of the membrane).

I get volume of cell without membrane = 5.222 x 10¹¹ nm³

So volume of membrane = 0.014 x 10¹¹ nm³ = 1.4 x 10⁹ nm³

Then for the last part, it will be (volume of membrane / cell volume) x 100. You can just use your answers from (a) to (b) for this. (I get 0.27 %)

Mike