The cost of paper is Rs. 55 per kg. If one kg of paper covers an area of `192 m^(2)`, what will be the cost in covering a cube of edge 8 metre ?

Options

A. Rs. 110
B. Rs. 165
C. Rs. 55
D. Rs. 192

Answer

To solve the problem, we need to find the cost of paper required to cover a cube with an edge of 8 meters. Here’s a step-by-step solution:

### Step 1: Calculate the Surface Area of the Cube
The formula for the surface area \( A \) of a cube with edge length \( a \) is given by:
\[ A = 6a^2 \]
For a cube with an edge of 8 meters:
\[ A = 6 \times (8)^2 = 6 \times 64 = 384 \, \text{m}^2 \]

### Step 2: Determine the Cost of Paper per Square Meter
We know that 1 kg of paper covers an area of 192 m² and costs Rs. 55. Therefore, the cost per square meter can be calculated as follows:
\[ \text{Cost per m}^2 = \frac{55 \, \text{Rs}}{192 \, \text{m}^2} \]

### Step 3: Calculate the Total Cost to Cover the Cube
Now, we need to find the total cost to cover the surface area of the cube, which is 384 m². We can use the unitary method:
\[ \text{Total Cost} = \text{Cost per m}^2 \times \text{Total Area} \]
Substituting the values:
\[ \text{Total Cost} = \left(\frac{55}{192}\right) \times 384 \]

### Step 4: Simplify the Calculation
Calculating the total cost:
\[ \text{Total Cost} = 55 \times \frac{384}{192} \]
Since \( \frac{384}{192} = 2 \):
\[ \text{Total Cost} = 55 \times 2 = 110 \, \text{Rs} \]

### Final Answer
The cost to cover the cube of edge 8 meters is Rs. 110.

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