The volume of air in a room is `204 m^(3)`. The height of the room is 6m. What is the floor area of the room ?

Options

A. `32 m^(2)`
B. `46 m^(2)`
C. `44 m^(2)`
D. `34 m^(2)`

Answer

To find the floor area of the room, we can use the formula for the volume of a cuboid, which is given by:

\[ \text{Volume} = \text{Length} \times \text{Breadth} \times \text{Height} \]

Given:
- Volume of the room = \( 204 \, m^3 \)
- Height of the room = \( 6 \, m \)

We can rearrange the formula to find the product of the length and breadth (which gives us the floor area):

\[ \text{Length} \times \text{Breadth} = \frac{\text{Volume}}{\text{Height}} \]

Substituting the known values into the equation:

\[ \text{Length} \times \text{Breadth} = \frac{204 \, m^3}{6 \, m} \]

Now, we perform the division:

\[ \text{Length} \times \text{Breadth} = \frac{204}{6} = 34 \, m^2 \]

Thus, the floor area of the room is:

\[ \text{Floor Area} = 34 \, m^2 \]

### Summary of Steps:
1. Write down the formula for the volume of a cuboid.
2. Rearrange the formula to find the product of length and breadth.
3. Substitute the known values into the rearranged formula.
4. Perform the division to find the floor area.