Question

An E. coli cell contains about 15,000 ribosomes, which carry out protein synthesis. Assuming ribosomes are spherical and have a diameter of 20.0 nm, calculate the fraction of the E. coli cell volume that is occupied by ribosomes.

Answer 1

14.57%

Step-by-step explanation:

From the previous lesson, we understood that the Volume of E.coli = 4.13 × 10⁻¹⁹ m³

The diameter of the ribosome = 20 nm

Radius will be D/2 = 20 nm/2 = 10 nm

The volume of the sphere since the shape of the ribosome is spherical = 4πr³

∴

The volume for each ribosome = 4πr³

For 15000 ribosome, we have:

`= 15000 * ((4)/(3)\pi) ((10^(-8))^3)`

`= 15000 * ((4)/(3)\pi) (10^(-24))`

= 6.283 × 10⁻²⁰

Thus, the fraction of E.coli volume occupied by the ribosome can be determined by using the formula:

`= (Vol. \ of \ ribosome)/(Vol. \ of \ E.coli)* 100`

`= (6.283 * 10^(-20))/(4.31 * 10^(-19))* 100`

= 14.57%