Question

simple cuboidal epithelial cells line the ducts of certain human exocrine glands. various materials are transported into or out of the cells by diffusion. (the formula for the surface area of a cube is 6×s², and the formula for the volume of a cube is s³, where s = the length of a side of the cube.) which of the following cube - shaped cells would be most efficient in removing waste by diffusion?

Explanation:

Step1: Recall the principle

Efficiency of diffusion is related to surface - area - to - volume ratio. Higher ratio means more efficient diffusion.

Step2: Calculate surface - area - to - volume ratio formula

For a cube with side length $S$, surface area $A = 6S^{2}$ and volume $V=S^{3}$. The surface - area - to - volume ratio $r=\frac{A}{V}=\frac{6S^{2}}{S^{3}}=\frac{6}{S}$.

Step3: Analyze each option

• Option A: $S = 10\mu m$, $r_A=\frac{6}{10}=0.6\mu m^{- 1}$.
• Option B: $S = 20\mu m$, $r_B=\frac{6}{20}=0.3\mu m^{- 1}$.
• Option C: $S = 30\mu m$, $r_C=\frac{6}{30}=0.2\mu m^{- 1}$.
• Option D: (not given side length, but as $S$ increases, $r$ decreases).

Since the ratio is highest for the smallest side - length, the cell with side length $10\mu m$ is most efficient.

Answer:

A. $10\mu m$