A suitcase with measures 80 cm `xx` 48 cm `xx` 24 cm is to be covered with a trapaulin cloth. How many metres of trapaulin of width 96 cm is required to cover 100 such suitcases ?

Answer

To find out how many meters of trapaulin cloth are required to cover 100 suitcases, we will follow these steps:

### Step 1: Calculate the Total Surface Area (TSA) of One Suitcase
The formula for the total surface area (TSA) of a cuboid is given by:
\[ \text{TSA} = 2(lb + bh + hl) \]
where:
- \( l = 80 \, \text{cm} \) (length)
- \( b = 48 \, \text{cm} \) (breadth)
- \( h = 24 \, \text{cm} \) (height)

Substituting the values into the formula:
\[ \text{TSA} = 2(80 \times 48 + 48 \times 24 + 24 \times 80) \]

Calculating each term:
- \( 80 \times 48 = 3840 \)
- \( 48 \times 24 = 1152 \)
- \( 24 \times 80 = 1920 \)

Now, add these values:
\[ 3840 + 1152 + 1920 = 6912 \]

Now multiply by 2:
\[ \text{TSA} = 2 \times 6912 = 13824 \, \text{cm}^2 \]

### Step 2: Calculate the Total Surface Area for 100 Suitcases
To find the total area required for 100 suitcases:
\[ \text{Total Area} = 100 \times \text{TSA of one suitcase} = 100 \times 13824 = 1382400 \, \text{cm}^2 \]

### Step 3: Calculate the Length of Trapaulin Cloth Required
The width of the trapaulin cloth is given as 96 cm. The area of the trapaulin cloth can be expressed as:
\[ \text{Area} = \text{Length} \times \text{Width} \]
Let \( L \) be the length of the trapaulin cloth. Therefore:
\[ L \times 96 = 1382400 \]

To find \( L \):
\[ L = \frac{1382400}{96} = 14400 \, \text{cm} \]

### Step 4: Convert Length from cm to m
Since 1 meter = 100 cm, we convert the length from centimeters to meters:
\[ L = \frac{14400}{100} = 144 \, \text{m} \]

### Final Answer
The total length of trapaulin cloth required to cover 100 suitcases is **144 meters**.

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