Answer:
SA:V of the bacterium to that of the amoeba [tex]= 300[/tex]
Explanation:
Surface area (SA) of a sphere [tex]= 4\pi r^2[/tex]
Volume (V) of a sphere [tex]= \frac{4}{3} \pi r^3[/tex]
Surface area to volume ratio is equal to
[tex]\frac{SA}{V} = \frac{4\pi r^2}{\frac{4}{3} \pi r^3} \\\frac{SA}{V} =\frac{3}{r}[/tex]
a) For bacteria of diameter [tex]= 0.5[/tex]μm [tex]= 0.5 * 0.001 = 0.0005[/tex]mm
[tex](\frac{SA}{V} )_1= \frac{3}{r} \\(\frac{SA}{V} )_1=\frac{3}{0.0005} \\[/tex]
[tex]= 6000[/tex]
This means there is [tex]6000[/tex] unit surface area per unit volume.
b) For amoeba with a diameter of [tex]150[/tex] μm[tex]= 150 * 0.001 = 0.15[/tex]mm
[tex](\frac{SA}{V} )_2= \frac{3}{r} \\(\frac{SA}{V} )_2=\frac{3}{0.15} \\[/tex]
[tex]= 20[/tex]
The ratio for SA:V of the bacterium to that of the amoeba
[tex]= \frac{6000}{20} \\= 300[/tex]
