A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the of the areas of the 4 walls, what is the volume of the hall?

Answer

To solve the problem step by step, we will follow the given information and use the formulas for the areas of the floor, ceiling, and walls, as well as the volume of the hall.

### Step-by-Step Solution

1. **Identify the dimensions of the hall:**
- Length (L) = 15 m
- Breadth (B) = 12 m

2. **Calculate the area of the floor and ceiling:**
- Area of the floor = Length × Breadth = 15 m × 12 m = 180 m²
- Area of the ceiling = Length × Breadth = 15 m × 12 m = 180 m²
- Total area of the floor and ceiling = Area of the floor + Area of the ceiling = 180 m² + 180 m² = 360 m²

3. **Set up the equation for the area of the walls:**
- The area of the 4 walls = 2 × Height (H) × (Length + Breadth)
- Area of the 4 walls = 2 × H × (15 m + 12 m) = 2 × H × 27 m = 54H m²

4. **According to the problem, the area of the floor and ceiling is equal to the area of the 4 walls:**
- So, we have the equation:
\[ 360 m² = 54H m² \]

5. **Solve for Height (H):**
- Rearranging the equation gives:
\[ H = \frac{360 m²}{54 m²} = \frac{360}{54} = \frac{20}{3} \text{ m} \]
- Thus, Height (H) = \( \frac{20}{3} \) m or approximately 6.67 m.

6. **Calculate the volume of the hall:**
- Volume (V) = Length × Breadth × Height
- Substitute the values:
\[ V = 15 m × 12 m × \frac{20}{3} m \]
- Calculate:
\[ V = 15 × 12 × \frac{20}{3} = 1800 ÷ 3 = 600 m³ \]

### Final Answer:
The volume of the hall is **600 m³**.