Question

Calculate the surface-to-volume ratio of a spherical cell 15mum in diameter and of a cell 2mum in diameter. What are the consequences of these differences in surface-to-volume ratio for cell functions?

Answer 1

For calculating the surface to volume ratio for a spherical cell,

Surface area (S) = 4πr²

Volume (V) = 4πr³ / 3

Ratio = S / V = 4πr² / 4πr³ / 3 = 3 × 4πr² / 4πr³

= 3/r

1. 15 micrometer diameter = Ratio = 3/7.5 = 0.4

2. 2 micrometer diameter = Ratio = 3/1 = 3

The cells exhibiting high surface to volume ratio shows enhanced metabolic activity. Shows easy uptake of oxygen, nutrients, water, and also the excretion of waste as they possess large surface.