The length of a hall is 20 metres and the width is 16 metres. The sum of the areas of the floor and roof is equal to the sum of the areas of the four walls. Find the volume of the hall.

### Concept & Volume of a Cuboid To find the volume of the hall, we first need to determine its height. The problem states a clear relationship between the areas of the top/bottom and the lateral surfaces (walls). $$ Volume = Length \times Breadth \times Height $$ $$ Area\_of\_Floor\_and\_Roof = 2 \times (Length \times Breadth) $$ $$ Area\_of\_Four\_Walls = 2 \times Height \times (Length + Breadth) $$ ### Step-by-Step Solution 1. **Given Data**: - Length (L) = 20 m - Width / Breadth (B) = 16 m 2. **Calculate Area of Floor and Roof**: - Area = 2 × (20 × 16) = 2 × 320 = 640 m² 3. **Set Up the Equation**: - The area of the four walls is 2H(L + B) = 2H(20 + 16) = 2H(36) = 72H - According to the condition: 72H = 640 4. **Find the Height (H)**: - H = 640 / 72 = 80 / 9 m 5. **Calculate Volume**: - Volume = L × B × H = 20 × 16 × (80 / 9) - Volume = 320 × (80 / 9) = 25600 / 9 - Volume ≈ 2844.44 m³ ### Exam Strategy & Shortcut When you reach the fraction 25600 / 9, realize that 25 + 6 = 11, which isn't divisible by 9, meaning it will be a recurring decimal. 25600 / 9 = 2844.44... Knowing the fraction breakdown instantly guides you to the correct choice without exhaustive division. ### Common Pitfall A frequent error is forgetting to multiply the floor area by 2 when equating it to the walls. "Floor and roof" implies two identical rectangular areas. ### Final Answer Therefore, the correct answer is **2844.4 m³**.