The area of the four walls of a room is 2640 sq. m and the length is twice the breadth and the height is given as 11 m. What is the area of the ceiling?

Options

A. `2800 m^2`
B. `3200 m^2`
C. `320 m^2`
D. none of these

Answer

To solve the problem step by step, we will follow the given information and apply the necessary formulas.

### Step 1: Understand the problem
We are given:
- The area of the four walls of a room is 2640 sq. m.
- The height of the room is 11 m.
- The length of the room is twice the breadth.

### Step 2: Define variables
Let the breadth of the room be \( x \) meters.
Then, the length of the room will be \( 2x \) meters.

### Step 3: Use the formula for the area of the four walls
The formula for the area of the four walls of a room is:
\[ \text{Area of 4 walls} = 2h(l + b) \]
Substituting the values we have:
\[ 2640 = 2 \cdot 11 \cdot (2x + x) \]

### Step 4: Simplify the equation
First, simplify the right side:
\[ 2640 = 22(3x) \]
\[ 2640 = 66x \]

### Step 5: Solve for \( x \)
Now, divide both sides by 66 to find \( x \):
\[ x = \frac{2640}{66} = 40 \text{ m} \]

### Step 6: Find the length
Now that we have the breadth \( x = 40 \) m, we can find the length:
\[ \text{Length} = 2x = 2 \cdot 40 = 80 \text{ m} \]

### Step 7: Calculate the area of the ceiling
The area of the ceiling can be calculated using the formula:
\[ \text{Area of ceiling} = \text{Length} \times \text{Breadth} \]
Substituting the values we found:
\[ \text{Area of ceiling} = 80 \times 40 = 3200 \text{ sq. m} \]

### Final Answer
The area of the ceiling is \( 3200 \) sq. m.

---