The length , breadth and height of box are 2m , 1.5 m and 80 cm respectively . What would be the cost of canvas to cover it up fully , if one square metre of canvas costs Rs. 25.00 ?

Options

A. Rs. 260
B. Rs. 290
C. Rs. 285
D. none of these

Answer

To solve the problem step by step, we need to find the total surface area of the box and then calculate the cost of the canvas required to cover it.

### Step 1: Convert all dimensions to the same unit
The dimensions given are:
- Length (l) = 2 m
- Breadth (b) = 1.5 m
- Height (h) = 80 cm

First, we convert the height from centimeters to meters:
\[ h = 80 \, \text{cm} = \frac{80}{100} \, \text{m} = 0.8 \, \text{m} \]

### Step 2: Calculate the total surface area of the box
The formula for the total surface area (SA) of a rectangular box is:
\[ SA = 2(lb + bh + hl) \]
Substituting the values we have:
- \( l = 2 \, \text{m} \)
- \( b = 1.5 \, \text{m} \)
- \( h = 0.8 \, \text{m} \)

Now, calculate each term:
1. \( lb = 2 \times 1.5 = 3 \, \text{m}^2 \)
2. \( bh = 1.5 \times 0.8 = 1.2 \, \text{m}^2 \)
3. \( hl = 0.8 \times 2 = 1.6 \, \text{m}^2 \)

Now, sum these areas:
\[ lb + bh + hl = 3 + 1.2 + 1.6 = 5.8 \, \text{m}^2 \]

Now, substitute this back into the surface area formula:
\[ SA = 2 \times 5.8 = 11.6 \, \text{m}^2 \]

### Step 3: Calculate the cost of the canvas
The cost of canvas per square meter is Rs. 25. Therefore, the total cost (C) to cover the box is:
\[ C = \text{SA} \times \text{cost per sqm} \]
Substituting the values:
\[ C = 11.6 \, \text{m}^2 \times 25 \, \text{Rs/m}^2 = 290 \, \text{Rs} \]

### Final Answer
The cost of the canvas to cover the box fully is Rs. 290.

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