The volume of a room is `378m^(3)` and the area of its floor is `84m^(2)`. Find the height of the room.

Answer

To find the height of the room given its volume and the area of its floor, we can follow these steps:

### Step 1: Understand the formulas
We know the formula for the volume of a rectangular room:
\[ \text{Volume} = \text{Area of the floor} \times \text{Height} \]
And the formula for the area of the floor:
\[ \text{Area} = \text{Length} \times \text{Breadth} \]

### Step 2: Write down the given values
From the problem, we have:
- Volume of the room = \( 378 \, m^3 \)
- Area of the floor = \( 84 \, m^2 \)

### Step 3: Set up the equation for height
Using the volume formula, we can express height as:
\[ \text{Height} = \frac{\text{Volume}}{\text{Area}} \]

### Step 4: Substitute the known values
Now, substitute the known values into the equation:
\[ \text{Height} = \frac{378 \, m^3}{84 \, m^2} \]

### Step 5: Perform the division
Now, calculate the height:
\[ \text{Height} = \frac{378}{84} \]

### Step 6: Simplify the fraction
To simplify \( \frac{378}{84} \):
- Dividing both the numerator and denominator by 42:
\[ \frac{378 \div 42}{84 \div 42} = \frac{9}{2} = 4.5 \]

### Step 7: State the final answer
Thus, the height of the room is:
\[ \text{Height} = 4.5 \, m \]

### Conclusion
The height of the room is \( 4.5 \, m \).

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