A godown is in the shape of a cuboid whose length, breadth and height are 56 m, 42 m and 10 m respectively. How many (maxiumum) cuboidal boxes each measuring `2.8 m xx 2.5 cm xx 70 cm` can be stored into the grodown?

Options

A. 5400
B. 2400
C. 3600
D. 4800

Answer

To find the maximum number of cuboidal boxes that can be stored in a godown shaped like a cuboid, we need to follow these steps:

### Step 1: Calculate the volume of the godown.
The volume \( V \) of a cuboid is given by the formula:
\[ V = \text{length} \times \text{breadth} \times \text{height} \]
Given dimensions:
- Length = 56 m
- Breadth = 42 m
- Height = 10 m

Calculating the volume:
\[ V_{\text{godown}} = 56 \, \text{m} \times 42 \, \text{m} \times 10 \, \text{m} \]
\[ V_{\text{godown}} = 23520 \, \text{m}^3 \]

### Step 2: Calculate the volume of one cuboidal box.
The volume \( V \) of a cuboidal box is also given by the formula:
\[ V = \text{length} \times \text{breadth} \times \text{height} \]
Given dimensions of the box:
- Length = 2.8 m
- Breadth = 2.5 cm = 0.025 m (convert cm to m)
- Height = 70 cm = 0.7 m (convert cm to m)

Calculating the volume:
\[ V_{\text{box}} = 2.8 \, \text{m} \times 0.025 \, \text{m} \times 0.7 \, \text{m} \]
\[ V_{\text{box}} = 0.049 \, \text{m}^3 \]

### Step 3: Calculate the maximum number of boxes that can fit in the godown.
To find the maximum number of boxes, divide the volume of the godown by the volume of one box:
\[ \text{Number of boxes} = \frac{V_{\text{godown}}}{V_{\text{box}}} \]
Substituting the values:
\[ \text{Number of boxes} = \frac{23520 \, \text{m}^3}{0.049 \, \text{m}^3} \]
Calculating this gives:
\[ \text{Number of boxes} \approx 480000 \]

### Conclusion
The maximum number of cuboidal boxes that can be stored in the godown is **480000**.

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