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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.

Respuesta :

Answer:

a) [tex]7243.6069\\[/tex]

b) [tex]9.0469[/tex]

c) [tex]0.1248[/tex]%

Explanation:

We know that 1 nm is equal to [tex]0.001[/tex]μm

Given,

a) Radius of human cell

[tex]= 12[/tex] μm

b) Thickness of cell membrane

[tex]= 5[/tex]nm [tex]= 0.005[/tex]μm

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

[tex]= 12 + 0.005\\= 12.005\\[/tex]μm

a) Volume of the cell including the membrane

[tex]\frac{4}{3} \pi r^{3} \\= \frac{4}{3} *(3.14)* (12.005)^{3}\\= 7243.6069[/tex] cubic μm

b) Volume of the cell membrane

Volume of cell without membrane

[tex]\frac{4}{3} \pi r^{3} \\= \frac{4}{3} *(3.14)* (12)^{3}\\= 7234.56[/tex] cubic μm

Volume of cell membrane only is equal to

[tex]7243.6069 - 7234.56\\= 9.0469[/tex] 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

[tex]\frac{9.0469}{7243.6069} * 100\\= 0.1248[/tex]%

batolisis

1) Volume of cell including the membrane = 9.07 * 10¹¹ nm³

2) Volume of cell membrane = 0.02 * 10¹¹ nm³

3) Percentage of total volume occupied by cell membrane = 0.22 %

Given data :

Diameter of human cell = 12.00 μm = 12,000 nm    i.e. radius = 6000 nm

thickness of membrane enclosing the human cell = 5.00 nm

∴ Total diameter of cell including membrane = 12,000 + ( 5 * 2 ) = 12010 nm

A) Determine the volume of the cell including the membrane

volume of cell ( sphere ) = [tex]\frac{4}{3}\pi r^{3}[/tex]  ----- ( 1 )

where :  r = 12010 / 2 = 6005 nm

back to equation ( 1 )

[tex]\frac{4}{3} * \pi * ( 6005 ) ^2[/tex]  = 9.07 * 10¹¹ nm³

B) Determine the volume of the cell membrane

(volume of cell and membrane ) -  ( volume of cell only )

= 9.07 * 10¹¹ nm³ - [ 4/3 * π * 6000³ ]

= ( 9.07 * 10¹¹ ) - ( 9.05 * 10¹¹ )

= 0.02 * 10¹¹ nm³

C) The percentage of total volume occupied by membrane

( volume of membrane / total volume of cell including membrane ) * 100

= [ 0.02 * 10¹¹  / 9.07 * 10¹¹ ] * 100

= 0.22%

Hence we can conclude that ;  Volume of cell including the membrane = 9.07 * 10¹¹ nm³,  Volume of cell membrane = 0.02 * 10¹¹ nm³ , Percentage of total volume occupied by cell membrane = 0.22  %.

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