Question

questions
calculate the surface to volume ratio of volume ratio of a e. coil bacterium with a surface area of 15 $\mu$m$^2$ and a volume of 5 $\mu$m$^3$.

Explanation:

Step1: Understand the ratio formula

The surface - to - volume ratio is calculated by dividing the surface area (\(S\)) by the volume (\(V\)). The formula for the surface - to - volume ratio \(R=\frac{S}{V}\).

Step2: Substitute the given values

We are given that the surface area \(S = 15\ \mu m^{2}\) and the volume \(V=5\ \mu m^{3}\). Substituting these values into the formula \(R = \frac{S}{V}\), we get \(R=\frac{15\ \mu m^{2}}{5\ \mu m^{3}}\).

Step3: Perform the division

When we divide \(15\) by \(5\), we get \(3\), and when we divide \(\mu m^{2}\) by \(\mu m^{3}\), using the rule of exponents \(a^{m}\div a^{n}=a^{m - n}\), we have \(\mu m^{2-3}=\mu m^{- 1}=\frac{1}{\mu m}\). So the ratio \(R = 3\ \mu m^{-1}\) or \(\frac{3}{\mu m}\).

Answer:

The surface - to - volume ratio is \(3\ \mu m^{-1}\) (or \(\frac{3}{\mu m}\))