Question

A typical human cell is approximately 12.00 μm in diameter and enclosed by a membrane that is 5.000 nm thick. (a) What is the volume of the cell including the membrane? (b) What is the volume of the cell membrane? (c) What percent of the total volume does its membrane occupy? To simplify the calculations, model the cell as a sphere. Enter your answers using four significant figures.

Answer 1

Answer:

a) $7243.6069$

b) $9.0469$

c) $0.1248$%

Explanation:

We know that 1 nm is equal to $0.001$μm

Given,

a) Radius of human cell

$= 12$ μm

b) Thickness of cell membrane

$= 5$nm $= 0.005$μm

c) Radius of human cell including the thickness of cell membrane

$= 12 + 0.005\\= 12.005$μm

a) Volume of the cell including the membrane

$\frac{4}{3} \pi r^{3} \\= \frac{4}{3} *(3.14)* (12.005)^{3}\\= 7243.6069$ cubic μm

b) Volume of the cell membrane

Volume of cell without membrane

$\frac{4}{3} \pi r^{3} \\= \frac{4}{3} *(3.14)* (12)^{3}\\= 7234.56$ cubic μm

Volume of cell membrane only is equal to

$7243.6069 - 7234.56\\= 9.0469$ cubic μm

b) What percent of the total volume does its membrane occupy

The percent of the total volume occupied by  its membrane is equal to

$\frac{9.0469}{7243.6069} * 100\\= 0.1248$%