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 (maximum) cuboidal boxes each measuring `2.8 mxx 2.5 m xx 70 cm` can be stored into the godown?

Options

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

Answer

To find out how many maximum cuboidal boxes can be stored in the godown, 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:
- Length = 56 m
- Breadth = 42 m
- Height = 10 m

Substituting the values:
\[ V_{\text{godown}} = 56 \, \text{m} \times 42 \, \text{m} \times 10 \, \text{m} \]

### Step 2: Calculate the Volume of One Box
The volume of the cuboidal box is also calculated using the same formula:
\[ V_{\text{box}} = \text{length} \times \text{breadth} \times \text{height} \]
Given:
- Length = 2.8 m
- Breadth = 2.5 m
- Height = 70 cm (which is equal to 0.7 m)

Substituting the values:
\[ V_{\text{box}} = 2.8 \, \text{m} \times 2.5 \, \text{m} \times 0.7 \, \text{m} \]

### Step 3: Calculate the Number of Boxes
To find the maximum number of boxes that can fit in the godown, we divide the volume of the godown by the volume of one box:
\[ \text{Number of boxes} = \frac{V_{\text{godown}}}{V_{\text{box}}} \]

### Step 4: Perform the Calculations
1. Calculate the volume of the godown:
\[ V_{\text{godown}} = 56 \times 42 \times 10 = 23520 \, \text{m}^3 \]

2. Calculate the volume of one box:
\[ V_{\text{box}} = 2.8 \times 2.5 \times 0.7 = 4.9 \, \text{m}^3 \]

3. Calculate the number of boxes:
\[ \text{Number of boxes} = \frac{23520}{4.9} \approx 4800 \]

### Conclusion
The maximum number of cuboidal boxes that can be stored in the godown is **4800**.

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