Question

A spherical bacterium has a diameter of 2 µm. Its volume to surface area ratio is equal to ............ µm (round off to 2 decimal places)

Hint:

The volume to surface area ratio for a sphere is the radius divided by 3.

Answer 1

Correct Answer: 0.32

Step 1: Formula for volume and surface area.
For a sphere, the volume \( V \) and surface area \( A \) are given by the following formulas: \[ V = \frac{4}{3} \pi r^3 \quad \text{and} \quad A = 4 \pi r^2 \] where \( r \) is the radius of the sphere.
The volume to surface area ratio is given by: \[ \text{Ratio} = \frac{V}{A} = \frac{\frac{4}{3} \pi r^3}{4 \pi r^2} = \frac{r}{3} \] where \( r \) is the radius.
Step 2: Find the radius.
The problem gives the diameter of the bacterium as 2 µm. Therefore, the radius is: \[ r = \frac{2}{2} = 1 \, \mu m \] Step 3: Calculate the volume to surface area ratio.
Using the formula for the volume to surface area ratio: \[ \text{Ratio} = \frac{r}{3} = \frac{1}{3} = 0.33 \, \mu m \] Step 4: Conclusion.
Thus, the volume to surface area ratio is \( \boxed{4.36} \) µm (rounded to two decimal places).