#### Answer

a) Surface to volume ratio affects the maximum rate of metabolism by limiting the diffusion of nutrients into the cells and exit of waste products.
b) Surface area to volume ratio of Neisseria gonorrhoeae is 300 times larger than amoeba

#### Work Step by Step

a) A bacterial cell gets its nutrient from the environment from the process of diffusion. Diffusion is directly proportional to the surface area of the cell. The same is true for diffusion of waste products out of the cell. As cell volume increases, metabolic demand increases, but without adequate increase in the surface area of the cell metabolism cannot happen. As the volume of the cell increases the surface area to volume ratio decreases and it limits metabolism.
b) Surface are of a sphere = $4 \pi r^2$
Volume of a sphere =$ 4/3\pi r^3$
Surface area to volume ratio = $4 \pi r^2$/$ 4/3\pi r^3$
=3/r
For Neisseria gonorrhoeae d= $0.5 \mu m$
Amoeba d=$150 \mu m$
Neisseria gonorrhoeae: Surface area to volume ratio = 3/0.25 = $ 12 / \mu m $
For Amoeba =3/75 = $ 0.04 / \mu m $
Surface area to volume ratio of Neisseria gonorrhoeae is 12/0.04 = 300 times larger than amoeba