Question

Consider the following geometric solids.

A sphere with a ratio of surface area to volume equal to 0.08 m-1.
A right circular cylinder with a ratio of surface area to volume equal to 2.1 m-1.
What results would you expect if these two models were compared in a diffusion test?

A. The rate of diffusion would be the same for the two models.
B. The rate of diffusion would be faster for the right cylinder.
C. The rate of diffusion would be slower for the right cylinder.
D. The rate of diffusion would be faster for the sphere.

Answer 1

B
The greater the surface area to volume ratio, the greater the rate of diffusion.

Answer 2

Before answering this question, first we have to understand the effect of ratio of surface area to volume on the rate of diffusion.

The rate of diffusion for a body having larger surface area as compared to the ratio of surface area to volume will be more than a body having less surface area. Mathematically it can written as-

V∝ R [ where v is the rate of diffusion and r is the ratio of surface area to volume]

As per the question,the ratio of surface area to volume for a sphere is given
`0.08m^(-1)`

The surface area to volume ratio for right circular cylinder is given
`2.1m^(-1)`

Hence, it is obvious that the ratio is more for right circular cylinder.As the rate diffusion is directly proportional to the surface area to volume ratio,hence rate of diffusion will be more for right circular cylinder.

Hence the correct option is B. The rate of diffusion would be faster for the right cylinder.