Introduction

The surface area to volume (SA/V) ratio is an important biological concept.
Smaller spherical bacteria like coccus have a higher SA/V ratio,
allowing faster diffusion of nutrients and gases.
Let us calculate the ratio for a spherical coccus of radius 0.8 μm.

Given

Radius (r) = 0.8 μm

Find:
Surface Area / Volume (μm^-1)

Step 1: Formula for Sphere

Surface Area (SA)

SA = 4πr²

Volume (V)

V = 4/3 πr³

Step 2: Take Ratio

SA / V = (4πr²) / ((4/3)πr³)

Cancel 4π

= r² / (1/3 r³)

= 3 / r

Shortcut Formula (Exam Trick)

For any sphere:

SA / V = 3 / r

Step 3: Substitute Value

SA / V = 3 / 0.8

= 3.75 μm^-1

Final Answer

3.75

Correct Option: (C)

Explanation of All Options

• (A) 7.45 – Too large, incorrect calculation
• (B) 4.05 – Formula error
• (C) 3.75 – Correct using 3/r
• (D) 0.85 – Inverse taken (V/SA)

Conceptual Understanding

SA/V ∝ 1/r

Smaller cells → Higher surface area to volume ratio → Faster nutrient exchange.