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 m × 2.5 m × 70 cm can be stored into the godown?

Question

Accepted Answer

To determine how many cuboidal boxes can be stored in the godown, we need to calculate the volume of both the godown and the boxes, and then see how many boxes fit into the godown.

1. **Volume of the Godown:**
   - The godown is in the shape of a cuboid with dimensions 56 m (length), 42 m (breadth), and 10 m (height).
   - Volume of the godown = Length × Breadth × Height = 56 m × 42 m × 10 m = 23,520 cubic meters.

2. **Volume of One Box:**
   - Each box has dimensions 2.8 m (length), 2.5 m (breadth), and 70 cm (height). Note that 70 cm needs to be converted to meters: 70 cm = 0.7 m.
   - Volume of one box = 2.8 m × 2.5 m × 0.7 m = 4.9 cubic meters.

3. **Number of Boxes that can be Stored:**
   - To find out how many such boxes can fit into the godown, divide the volume of the godown by the volume of one box.
   - Number of boxes = Volume of the godown / Volume of one box = 23,520 cubic meters / 4.9 cubic meters ≈ 4800.

Thus, the maximum number of cuboidal boxes that can be stored in the godown is 4800, which corresponds to Option 3.

**Explanation for Other Options:**

- **Option 1 (2400):** This number is too low. If we calculate the number of boxes based on the volumes, 2400 boxes would only occupy 11,760 cubic meters, which is only half of the godown's capacity. Therefore, this option is incorrect.

- **Option 2 (3600):** This number is also too low. 3600 boxes would occupy 17,640 cubic meters, which is still less than the total volume of the godown. Hence, this option is incorrect.

- **Option 4 (5400):** This number is too high. 5400 boxes would require 26,460 cubic meters, which exceeds the godown's capacity of 23,520 cubic meters. Therefore, this option is incorrect.

In conclusion, the correct answer is Option 3, as it accurately reflects the maximum number of boxes that can be stored in the godown based on the given dimensions.