A cube shaped cell has a side of 2 µm. It grows until its side is 6 µm…

Step 1. Surface area. $3^2 = 9$ times: from $24$ to $216\ \mu\text{m}^2$.

Step 2. Volume. $3^3 = 27$ times: from $8$ to $216\ \mu\text{m}^3$.

Step 3. Ratio. From $\dfrac{6}{2} = 3$ to $\dfrac{6}{6} = 1$ per µm: a third, $0.333$ of what it was.