A room has dimensions of 5 m × 4 m × 3 m. What is the total surface ar...
Understanding Room Dimensions
The room has dimensions of 5 m (length) × 4 m (width) × 3 m (height). To find the total surface area while excluding the floor, we will calculate the areas of the four walls and the ceiling.
Calculating the Areas of Walls
1. Area of Two Longer Walls (Length × Height):
- Each wall's area = Length × Height = 5 m × 3 m = 15 m²
- Total for two walls = 2 × 15 m² = 30 m²
2. Area of Two Shorter Walls (Width × Height):
- Each wall's area = Width × Height = 4 m × 3 m = 12 m²
- Total for two walls = 2 × 12 m² = 24 m²
Calculating the Area of the Ceiling
3. Area of the Ceiling (Length × Width):
- Ceiling area = Length × Width = 5 m × 4 m = 20 m²
Summing Up the Areas
4. Total Surface Area Calculation:
- Total wall area = Area of longer walls + Area of shorter walls = 30 m² + 24 m² = 54 m²
- Adding the ceiling area = Total wall area + Ceiling area = 54 m² + 20 m² = 74 m²
However, since we need to exclude the floor, we only consider the walls and the ceiling:
Final Calculation
- Total area excluding the floor = 54 m² (walls) + 20 m² (ceiling) = 74 m²
Conclusion
The total surface area of the room, excluding the floor, is 54 m². Therefore, the correct answer is option 'C'.
A room has dimensions of 5 m × 4 m × 3 m. What is the total surface ar...
The total surface area of the walls is calculated as 2(l × h) + 2(b × h). Using the dimensions, Total Surface Area = 2(5 × 3) + 2(4 × 3) = 30 + 24 = 54 m².