The internal dimensions of a box are 1.2 m 80 cm and 50 cm. How many cubes each of edge 7 cm can be packed in the box with faces parallel to the sides of the box.

Answer

To find out how many cubes of edge 7 cm can be packed into a box with internal dimensions of 1.2 m, 80 cm, and 50 cm, we will follow these steps:

### Step 1: Convert all dimensions to the same unit
First, we need to convert the dimensions of the box from meters and centimeters to centimeters.

- Length: 1.2 m = 120 cm (since 1 m = 100 cm)
- Breadth: 80 cm (already in cm)
- Height: 50 cm (already in cm)

So, the internal dimensions of the box are:
- Length = 120 cm
- Breadth = 80 cm
- Height = 50 cm

### Step 2: Determine how many cubes fit along each dimension
Next, we will calculate how many cubes of edge 7 cm can fit along each dimension of the box.

- For Length:
\[ \text{Number of cubes along length} = \frac{\text{Length}}{\text{Edge of cube}} = \frac{120 \text{ cm}}{7 \text{ cm}} \approx 17.14 \]
Since we can only fit whole cubes, we take the floor value, which is 17.

- For Breadth:
\[ \text{Number of cubes along breadth} = \frac{\text{Breadth}}{\text{Edge of cube}} = \frac{80 \text{ cm}}{7 \text{ cm}} \approx 11.43 \]
Again, taking the floor value gives us 11.

- For Height:
\[ \text{Number of cubes along height} = \frac{\text{Height}}{\text{Edge of cube}} = \frac{50 \text{ cm}}{7 \text{ cm}} \approx 7.14 \]
The floor value here is 7.

### Step 3: Calculate the total number of cubes
Now, we multiply the number of cubes that can fit along each dimension to find the total number of cubes that can be packed in the box.

\[ \text{Total number of cubes} = (\text{Number of cubes along length}) \times (\text{Number of cubes along breadth}) \times (\text{Number of cubes along height}) \]
\[ \text{Total number of cubes} = 17 \times 11 \times 7 \]
Calculating this gives:
\[ 17 \times 11 = 187 \]
\[ 187 \times 7 = 1309 \]

Thus, the total number of cubes that can be packed in the box is **1309**.