Answer to Question #232356 in General Chemistry for eja

Question

A typical human cell is approximately 11.00μm

11.00μm in diameter and enclosed by a membrane that is 5.00 nm

5.00 nm thick.

What is the total volume 𝑉

V of the cell, including the membrane? To simplify the calculations, model the cell as a sphere.

𝑉=

V=

μm

3

μm3

What is the volume 𝑉

membrane

Vmembrane of the cell membrane?

𝑉

membrane

=

Vmembrane=

μm

3

μm3

What percentage 𝑃

membrane

Pmembrane of the total volume does the membrane occupy?

Answer 1

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