Cell and membrane volume physics

[Akewal]

Homework Statement

A typical human cell is approximately 10 μm in diameter and enclosed by a membrane that is 4.2 nm thick. To simplify the calculations, model the cell as a sphere.
1) What is the volume of cell? (in μm^3)
2) What is the volume of cell membrane? (in μm^3)
3) Percent cell volume the membrane occupies

Homework Equations

V= 4/3*pi*r^3

The Attempt at a Solution

I knew the volume of sphere, so I could easily solve for number 1 Because 10 was the diameter, I divided it by 2 which gave me a radius of 5.
1) 4/3*pi*125= 523.60μm^3
2) This is where I got stuck. I converted 4.2 nm to μm (multiplying 4.2 with 0.001), and used the volume formula, with .0042 μm as my r. The answer is wrong!

What I am doing wrong?

 

[BvU]

Hello Akewal, $\qquad$$\qquad$!

The way you describe it, you calculated the volume of a sphere with a radius of 4.2 nm ...

If you make a coarse sketch, you see that you are after the volume of a shell with radius 5 $\mu$m and a thickness of 4.2 nm ... A different beast !