# DBT JRF 2022 — Question 47

Exam: DBT JRF 2022 · Section: A · Topic: Biochemistry › Surface Area to Volume Ratio · Difficulty: Medium

## Question

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. ![figure](https://res.cloudinary.com/dxil5euku/image/upload/v1779453117/pyq/6a104cb5920734408bc0c6d8/DBTJRF22-IMGA47%28i%29.png) ![figure](https://res.cloudinary.com/dxil5euku/image/upload/v1779453117/pyq/6a104cb5920734408bc0c6d8/DBTJRF22-IMGA47%28ii%29.png) ![figure](https://res.cloudinary.com/dxil5euku/image/upload/v1779453120/pyq/6a104cb5920734408bc0c6d8/DBTJRF22-IMGA47%28iii%29.png) ![figure](https://res.cloudinary.com/dxil5euku/image/upload/v1779453120/pyq/6a104cb5920734408bc0c6d8/DBTJRF22-IMGA47%28iv%29.png)

## Options

- **A.** A
- **B.** B
- **C.** C
- **D.** D

## 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 ![figure](https://res.cloudinary.com/dxil5euku/image/upload/v1779453117/pyq/6a104cb5920734408bc0c6d8/DBTJRF22-IMGA47%28i%29.png) , 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).

Source: https://mypyqbuddy.com/questions/which-one-of-these-cubes-labelled-a---6a104cd5920734408bc0c70c