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

Answer:

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

Explanation:

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

Volume (V) of a sphere $= \frac{4}{3} \pi r^3$

Surface area to volume ratio is equal to

$\frac{SA}{V} = \frac{4\pi r^2}{\frac{4}{3} \pi r^3} \\\frac{SA}{V} =\frac{3}{r}$

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

$(\frac{SA}{V} )_1= \frac{3}{r} \\(\frac{SA}{V} )_1=\frac{3}{0.0005}$

$= 6000$

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

$(\frac{SA}{V} )_2= \frac{3}{r} \\(\frac{SA}{V} )_2=\frac{3}{0.15}$

$= 20$

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

$= \frac{6000}{20} \\= 300$