Q.24 A bacterium belonging to cocci group has a diameter of 2 µm. The numerical value of the ratio of
its surface area to volume (in µm−1) is ________
Bacterium Cocci 2 µm Diameter: Surface Area to Volume Ratio Numerical Value
The surface area to volume (SA/V) ratio for a spherical coccus bacterium with 2 µm diameter is 3 µm⁻¹.
This fundamental calculation is crucial for understanding nutrient diffusion efficiency in bacterial cells and frequently appears in competitive exams like CSIR NET, GATE Biotechnology, and microbiology entrance tests.
SA/V Formula for Spherical Bacteria
Cocci bacteria approximate perfect spheres. For diameter = 2 µm, radius r = 1 µm.
Volume V = (4/3)πr³ = (4/3)π(1)³ = 4.19 µm³
SA/V ratio = 3/r = 3/1 = 3 µm⁻¹
Python computation confirms exact values: SA ≈ 12.57 µm², V ≈ 4.19 µm³, ratio = 3.0 µm⁻¹.
MCQ Options Analysis
Common multiple-choice options for this question: 0, 1, 2, 3
Biological Significance
The high SA/V ratio of 3 µm⁻¹ enables efficient nutrient uptake and waste removal through diffusion, a key evolutionary advantage for bacteria over larger eukaryotic cells.
Smaller cells maintain higher ratios, explaining why prokaryotes thrive in nutrient-limited environments compared to larger cells with lower SA/V ratios.
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