The dimensions of a classroom are 12 m, 6 m, and 4 m. Find the cost of decorating its walls by a wallpater of 50 cm width, which costs Rs.30 per metre.

Options

A. Rs.8600
B. Rs.8460
C. Rs.8640
D. Rs.8600

Explanation

To solve the problem, we need to follow these steps:

### Step 1: Calculate the Surface Area of the Walls
The classroom has four walls, and we can calculate the total surface area of these walls using the formula:
\[ \text{Total Surface Area} = 2 \times (Length \times Height + Width \times Height) \]
Given:
- Length (L) = 12 m
- Width (W) = 6 m
- Height (H) = 4 m

Substituting the values:
\[ \text{Total Surface Area} = 2 \times (12 \times 4 + 6 \times 4) \]
Calculating the areas:
\[ = 2 \times (48 + 24) = 2 \times 72 = 144 \text{ m}^2 \]

### Step 2: Calculate the Area Covered by One Roll of Wallpaper
The width of the wallpaper is given as 50 cm. To convert this to meters:
\[ 50 \text{ cm} = \frac{50}{100} = 0.5 \text{ m} \]
Now, the area covered by 1 meter of wallpaper (which is 1 m long and 0.5 m wide) is:
\[ \text{Area of wallpaper per meter} = 1 \times 0.5 = 0.5 \text{ m}^2 \]

### Step 3: Calculate the Total Length of Wallpaper Needed
To find out how many meters of wallpaper we need, we divide the total surface area of the walls by the area covered by 1 meter of wallpaper:
\[ \text{Total Length of Wallpaper} = \frac{\text{Total Surface Area}}{\text{Area of wallpaper per meter}} = \frac{144}{0.5} = 288 \text{ m} \]

### Step 4: Calculate the Cost of the Wallpaper
The cost of wallpaper is Rs. 30 per meter. Therefore, the total cost will be:
\[ \text{Total Cost} = \text{Total Length of Wallpaper} \times \text{Cost per meter} = 288 \times 30 = 8640 \text{ Rs} \]

### Final Answer
The cost of decorating the walls of the classroom is **Rs. 8640**.

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