A closed box is a cuboid in shape with length = 40 cm , breadth = 30 cm and height = 50 cm , It is made of thin metal sheet. Find the cost of metal sheets required to make 20 such boxes. If ` 1m ^(2)` of metal sheet costs rupes 45.

Answer

To find the cost of metal sheets required to make 20 closed boxes (cuboids) with given dimensions, we will follow these steps:

### Step 1: Calculate the Total Surface Area of One Box
The formula for the total surface area (TSA) of a cuboid is given by:
\[ \text{TSA} = 2 \times (l \times b + b \times h + h \times l) \]
Where:
- \( l \) = length
- \( b \) = breadth
- \( h \) = height

Given:
- Length \( l = 40 \, \text{cm} \)
- Breadth \( b = 30 \, \text{cm} \)
- Height \( h = 50 \, \text{cm} \)

Substituting the values into the formula:
\[ \text{TSA} = 2 \times (40 \times 30 + 30 \times 50 + 50 \times 40) \]

Calculating each term:
- \( 40 \times 30 = 1200 \)
- \( 30 \times 50 = 1500 \)
- \( 50 \times 40 = 2000 \)

Now, adding these:
\[ 1200 + 1500 + 2000 = 4700 \]

Now, calculating the total surface area:
\[ \text{TSA} = 2 \times 4700 = 9400 \, \text{cm}^2 \]

### Step 2: Calculate the Cost of Metal Sheets for One Box
The cost of metal sheets is given as Rs. 45 per square meter. First, we need to convert the area from square centimeters to square meters:
\[ 1 \, \text{m}^2 = 10000 \, \text{cm}^2 \]
So,
\[ \text{Area in m}^2 = \frac{9400 \, \text{cm}^2}{10000} = 0.94 \, \text{m}^2 \]

Now, calculate the cost for one box:
\[ \text{Cost for one box} = \text{Area in m}^2 \times \text{Cost per m}^2 = 0.94 \times 45 \]
Calculating this:
\[ 0.94 \times 45 = 42.3 \, \text{Rs} \]

### Step 3: Calculate the Cost for 20 Boxes
Now, to find the total cost for 20 boxes:
\[ \text{Total Cost} = \text{Cost for one box} \times 20 = 42.3 \times 20 \]
Calculating this:
\[ 42.3 \times 20 = 846 \, \text{Rs} \]

### Final Answer
The cost of metal sheets required to make 20 such boxes is Rs. 846.

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