Which one of these cubes (labelled A - D) will have the highest surface to volume ratio? The length of sides of each cube are given in cm. [Image]…

Which one of these cubes (labelled A - D) will have the highest surface to volume ratio? The length of sides of each cube are given in cm.

Select an option to attempt

1. A
   A
2. B
   B
3. C
   C
4. D
   D

Correct Answer: Option D

Explanation

Surface-to-volume ratio of cubes:For a cube with side length$a$:$\text{Surface area} = 6a^2$,$\text{Volume} = a^3$$\text{Surface-to-volume ratio} = \frac{6a^2}{a^3} = \frac{6}{a}$This ratio is INVERSELY proportional to the side length: smaller cube → larger ratio.From the image

, Cube D has the smallest side length among A, B, C, D, hence the highest surface-to-volume ratio.Biological significance: Cells also have a limited S:V ratio, which is why very large cells cannot efficiently exchange nutrients and waste.Answer: Cube D (Option 4).