Question

The bacterium Neisseria gonorrhoeae, which is responsible for the disease gonorrhea, has a diameter of 0.5 μm. Assuming a spherical shape in both cases, calculate the surface area to volume ratio of the bacterium, as well as that of a large, eukaryotic globular amoeba with a diameter of 150 μm. Compare the SA:V of the bacterium to that of the amoeba.

Answer 1

SA:V of the bacterium to that of the amoeba
`= 300`

Step-by-step explanation:

Surface area (SA) of a sphere
`= 4\pi r^2`

Volume (V) of a sphere
`= (4)/(3) \pi r^3`

Surface area to volume ratio is equal to

`(SA)/(V) = (4\pi r^2)/((4)/(3) \pi r^3) \\(SA)/(V) =(3)/(r)`

a) For bacteria of diameter
`= 0.5`μm
`= 0.5 * 0.001 = 0.0005`mm

`((SA)/(V) )_1= (3)/(r) \\((SA)/(V) )_1=(3)/(0.0005) \\`

`= 6000`

This means there is
`6000` unit surface area per unit volume.

b) For amoeba with a diameter of
`150` μm
`= 150 * 0.001 = 0.15`mm

`((SA)/(V) )_2= (3)/(r) \\((SA)/(V) )_2=(3)/(0.15) \\`

`= 20`

The ratio for SA:V of the bacterium to that of the amoeba

`= (6000)/(20) \\= 300`