A hall is 18 m long and 12 m broad. If the area of the floor is equal to the sum of the areas of the four walls, the volume (in `m^(3)`) of the hall is:

Options

A. 876.2
B. 777.6
C. 576.4
D. 675.5

Answer

To find the volume of the hall given the dimensions and the relationship between the area of the floor and the area of the walls, we can follow these steps:

### Step 1: Calculate the Area of the Floor
The area of the floor can be calculated using the formula for the area of a rectangle:
\[ \text{Area of the Floor} = \text{Length} \times \text{Breadth} \]
Given:
- Length = 18 m
- Breadth = 12 m

Substituting the values:
\[ \text{Area of the Floor} = 18 \, \text{m} \times 12 \, \text{m} = 216 \, \text{m}^2 \]

### Step 2: Set Up the Equation for the Area of the Four Walls
According to the problem, the area of the floor is equal to the sum of the areas of the four walls. The formula for the area of the four walls is:
\[ \text{Area of the Four Walls} = 2h(L + B) \]
Where:
- \( h \) = height of the hall
- \( L \) = length of the hall
- \( B \) = breadth of the hall

Since we know the area of the floor is 216 m², we can set up the equation:
\[ 2h(18 + 12) = 216 \]

### Step 3: Simplify the Equation
First, calculate \( 18 + 12 \):
\[ 18 + 12 = 30 \]
Now substitute this back into the equation:
\[ 2h \times 30 = 216 \]

### Step 4: Solve for Height \( h \)
Now simplify the equation:
\[ 60h = 216 \]
To find \( h \), divide both sides by 60:
\[ h = \frac{216}{60} = 3.6 \, \text{m} \]

### Step 5: Calculate the Volume of the Hall
The volume of the hall can be calculated using the formula:
\[ \text{Volume} = \text{Length} \times \text{Breadth} \times \text{Height} \]
Substituting the known values:
\[ \text{Volume} = 18 \, \text{m} \times 12 \, \text{m} \times 3.6 \, \text{m} \]
Calculating this gives:
\[ \text{Volume} = 216 \, \text{m}^2 \times 3.6 \, \text{m} = 777.6 \, \text{m}^3 \]

### Final Answer
The volume of the hall is:
\[ \boxed{777.6 \, \text{m}^3} \]