A godown is 15m long and 12 m broad. The sum of the area of the floor and the ceiling is equal to the sum of areas of the four walls. The volume (in `m^(3)`) of the godown is :

Options

A. 900
B. 1200
C. 1800
D. 720

Answer

To find the volume of the godown, we can follow these steps:

### Step 1: Identify the dimensions of the godown
The length (L) is given as 15 m and the breadth (B) is given as 12 m.

### Step 2: Calculate the area of the floor and the ceiling
The area of the floor (A_floor) is calculated as:
\[ A_{\text{floor}} = L \times B = 15 \, \text{m} \times 12 \, \text{m} = 180 \, \text{m}^2 \]

Since the area of the ceiling is the same as the area of the floor, the total area of the floor and ceiling (A_total) is:
\[ A_{\text{total}} = A_{\text{floor}} + A_{\text{ceiling}} = 180 \, \text{m}^2 + 180 \, \text{m}^2 = 360 \, \text{m}^2 \]

### Step 3: Calculate the area of the four walls
The area of the four walls (A_walls) can be calculated using the formula:
\[ A_{\text{walls}} = 2 \times (L + B) \times H \]

### Step 4: Set up the equation based on the problem statement
According to the problem, the sum of the area of the floor and ceiling is equal to the sum of the area of the four walls:
\[ A_{\text{total}} = A_{\text{walls}} \]
\[ 360 \, \text{m}^2 = 2 \times (L + B) \times H \]

### Step 5: Substitute the values of L and B
Substituting L = 15 m and B = 12 m:
\[ 360 = 2 \times (15 + 12) \times H \]
\[ 360 = 2 \times 27 \times H \]
\[ 360 = 54H \]

### Step 6: Solve for H (height)
To find H, divide both sides by 54:
\[ H = \frac{360}{54} = \frac{20}{3} \, \text{m} \]

### Step 7: Calculate the volume of the godown
The volume (V) of the godown is given by the formula:
\[ V = L \times B \times H \]
Substituting the values:
\[ V = 15 \, \text{m} \times 12 \, \text{m} \times \frac{20}{3} \, \text{m} \]
\[ V = 180 \times \frac{20}{3} = \frac{3600}{3} = 1200 \, \text{m}^3 \]

### Final Answer
The volume of the godown is **1200 m³**.

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