A cuboidal tea packet measures 10 cm by 6 cm by 4 cm. How many such tea packets can be placed in a cardboard box of dimensions 50 cm by 30 cm by 0.2 m?

Answer

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

### Step 1: Calculate the volume of the tea packet.
The dimensions of the tea packet are given as:
- Length = 10 cm
- Width = 6 cm
- Height = 4 cm

The volume \( V \) of a cuboid is calculated using the formula:
\[ V = \text{Length} \times \text{Width} \times \text{Height} \]
Substituting the values:
\[ V = 10 \, \text{cm} \times 6 \, \text{cm} \times 4 \, \text{cm} = 240 \, \text{cm}^3 \]

### Step 2: Calculate the volume of the cardboard box.
The dimensions of the cardboard box are given as:
- Length = 50 cm
- Width = 30 cm
- Height = 0.2 m

First, we need to convert the height from meters to centimeters:
\[ 0.2 \, \text{m} = 0.2 \times 100 = 20 \, \text{cm} \]

Now, we can calculate the volume of the cardboard box:
\[ V = \text{Length} \times \text{Width} \times \text{Height} \]
Substituting the values:
\[ V = 50 \, \text{cm} \times 30 \, \text{cm} \times 20 \, \text{cm} = 30000 \, \text{cm}^3 \]

### Step 3: Calculate how many tea packets can fit in the cardboard box.
To find out how many tea packets can fit, we divide the volume of the cardboard box by the volume of one tea packet:
\[ \text{Number of tea packets} = \frac{\text{Volume of cardboard box}}{\text{Volume of tea packet}} = \frac{30000 \, \text{cm}^3}{240 \, \text{cm}^3} \]

Calculating this gives:
\[ \text{Number of tea packets} = 125 \]

### Final Answer:
Thus, **125 tea packets** can be placed in the cardboard box.

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