8 persons can stay in a cubical room. Each person requires 27 m³ of air. The side of the cube is

6m

$\text{Total Volume} = \text{Number of persons} \times \text{Air required per person}$

$\text{Total Volume} = 8 \times 27\text{ m}^3 = 216\text{ m}^3$

Since the room is cubical, its volume ($V$) is given by the formula:

$V = \text{side}^3$

Now, we find the cube root of the total volume to get the side length:

$\text{side} = \sqrt[3]{216} = 6\text{ m}$