A carboard box is 1.2 m long, 72 cm wide and 54 cm high. How many bars of soap can be put into it if each bar measures `6 cm xx 4.5 cm xx 4 cm`?

Answer

To solve the problem of how many bars of soap can fit into a cardboard box, we will follow these steps:

### Step 1: Convert the dimensions of the box to the same unit
The dimensions of the cardboard box are given as:
- Length = 1.2 m
- Width = 72 cm
- Height = 54 cm

First, we need to convert the length from meters to centimeters:
1 meter = 100 centimeters
So,
\[ \text{Length} = 1.2 \, \text{m} \times 100 = 120 \, \text{cm} \]

### Step 2: Calculate the volume of the cardboard box
The formula for the volume of a rectangular box is:
\[ \text{Volume} = \text{Length} \times \text{Width} \times \text{Height} \]
Substituting the dimensions:
\[ \text{Volume of the box} = 120 \, \text{cm} \times 72 \, \text{cm} \times 54 \, \text{cm} \]
Calculating this:
\[ \text{Volume of the box} = 120 \times 72 \times 54 = 466560 \, \text{cm}^3 \]

### Step 3: Calculate the volume of one bar of soap
The dimensions of one bar of soap are:
- Length = 6 cm
- Width = 4.5 cm
- Height = 4 cm

Using the volume formula:
\[ \text{Volume of one soap bar} = 6 \, \text{cm} \times 4.5 \, \text{cm} \times 4 \, \text{cm} \]
Calculating this:
\[ \text{Volume of one soap bar} = 6 \times 4.5 \times 4 = 108 \, \text{cm}^3 \]

### Step 4: Calculate the number of soap bars that can fit in the box
To find the number of bars of soap that can fit into the box, we divide the volume of the box by the volume of one bar of soap:
\[ \text{Number of bars} = \frac{\text{Volume of the box}}{\text{Volume of one soap bar}} \]
Substituting the volumes:
\[ \text{Number of bars} = \frac{466560 \, \text{cm}^3}{108 \, \text{cm}^3} \]
Calculating this:
\[ \text{Number of bars} = 4320 \]

### Final Answer
Therefore, the number of bars of soap that can be put into the cardboard box is **4320**.

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