A wooden box of dimensions 8 metre `xx` 7 metres `xx` 6 metres is to carry rectangular boxes of dimensions `8 cm xx 7 cm xx 6 cm`. The maximum number of boxes that can be carried in 1 wooden box is

Options

A. 7500000
B. 9800000
C. 1200000
D. 1000000

Answer

To find the maximum number of smaller boxes that can fit into the larger wooden box, we need to calculate the volume of both the wooden box and the smaller boxes, and then divide the volume of the wooden box by the volume of one smaller box.

### Step 1: Calculate the volume of the wooden box.
The formula for the volume of a rectangular box is:
\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]

For the wooden box:
- Length = 8 meters
- Width = 7 meters
- Height = 6 meters

Convert the dimensions from meters to centimeters (since the smaller boxes are in centimeters):
- 1 meter = 100 centimeters
- Length = 8 m = 800 cm
- Width = 7 m = 700 cm
- Height = 6 m = 600 cm

Now calculate the volume:
\[ \text{Volume of wooden box} = 800 \, \text{cm} \times 700 \, \text{cm} \times 600 \, \text{cm} \]

### Step 2: Calculate the volume of one smaller box.
For the smaller box:
- Length = 8 cm
- Width = 7 cm
- Height = 6 cm

Now calculate the volume:
\[ \text{Volume of smaller box} = 8 \, \text{cm} \times 7 \, \text{cm} \times 6 \, \text{cm} \]

### Step 3: Calculate the volumes.
1. Volume of wooden box:
\[ \text{Volume of wooden box} = 800 \times 700 \times 600 = 336000000 \, \text{cm}^3 \]

2. Volume of smaller box:
\[ \text{Volume of smaller box} = 8 \times 7 \times 6 = 336 \, \text{cm}^3 \]

### Step 4: Calculate the maximum number of smaller boxes that can fit.
To find the maximum number of smaller boxes that can fit into the wooden box, divide the volume of the wooden box by the volume of one smaller box:
\[ \text{Maximum number of boxes} = \frac{\text{Volume of wooden box}}{\text{Volume of smaller box}} \]
\[ \text{Maximum number of boxes} = \frac{336000000 \, \text{cm}^3}{336 \, \text{cm}^3} \]

### Step 5: Perform the division.
\[ \text{Maximum number of boxes} = 1000000 \]

Thus, the maximum number of smaller boxes that can be carried in one wooden box is **1,000,000**.

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