How do i answer this?

Question

The dimensions of a prokaryotic ribosome are approximately 14 nm x 20 nm. If ribosomes occupy 20% of the volume of a bacterial cell calculate how many ribosomes are in a typical cell such as E. coli. Assume that the shape of a ribosome is approximately that of a cylinder. A typical bacterial cell volume is 1.6 um³.

Answer 1

Here are a few formulas we should be familiar with for this question:

Volume of a Cylinder = π*r²*h

1μm = 1000nm

First, we need to calculate 20% of the bacterial volume to understand how much volume ALL of the ribosomes will occupy:

0.2(1.6μm³) = 0.32μm³

Next, we should identify how much volume a single ribosome occupies:

Volume of a Cylinder = π*r²*h

Because the dimensions of the ribosome are 14x20nm we can say the width = 14nm and the height = 20 nm. The next part is a bit tricky because we need to find the radius of the cylinder in a roundabout manner. The following link explains how to calculate the radius, and we can use the same approach for this problem:

https://www.teachoo.com/9401/2124/Example-11/category/Examples/

Finding r of ribosome cylinder

The circumference of the cylinder = 14nm.

C = 2πr

r = C/2π = 14/(2π)

r = 2.23nm

As such, the volume of the ribosome should be:

V = π*r²*h

V = π*(2.23nm)²*(20nm)

V = 312.46nm³

We need to convert this into cubic micrometers:

1nm = 1000μm

1nm³ = 1 x 10⁹ μm

So to convert from nm to μm, we should divide by 10^9.

This gives us: 3.12 x 10^-7 μm for the volume of a single ribosome.

Finally, we should find the number of ribosomes in the bacterial cell.

We know that the volume that the ribosomes occupy is 0.32μm.

Dividing this by the volume of a single ribosome gives us:

0.32μm/3.12 x 10^-7 μm = 102,564 ribosomes.

Hopefully this makes sense!