How to Calculate the Height of a Smaller Refrigerator Given Its Similar Larger Counterpart

During a discussion, a question was posed regarding the calculation of the height of two similar refrigerators. The question stated that a larger refrigerator had a weight of 35 kg and a height of 15 meters, while a smaller refrigerator contained 20 kg of food, and their sizes were similar. The challenge was to determine the height of the smaller refrigerator.

Assumptions and Calculations

To tackle this problem, let's make a few reasonable assumptions:

Uniform Density: Both refrigerators contain homogeneous food items, meaning the density (kg/m3) of the food is the same in both refrigerators. Full Capacity: Each refrigerator is completely full, meaning the food fills up the available volume. Similitude: The only difference between the two refrigerators is their height, with identical floor footprints.

Given these assumptions, the volume of the larger refrigerator can be calculated as follows:

The larger refrigerator contains 35 kg of food, while the smaller one contains 20 kg. Since density is uniform, the volume of the larger refrigerator is directly proportional to its weight. Therefore, the volume of the larger refrigerator is 35 units and that of the smaller one is 20 units.

Calculating the Height Ratio

When comparing the heights of the two refrigerators, we can use the volume ratio to find the height of the smaller refrigerator:

The height of the larger refrigerator is 15 meters. The volume of the smaller refrigerator is (frac{20}{35}) times that of the larger refrigerator. Therefore, the height of the smaller refrigerator can be calculated as:

Height of the smaller refrigerator (frac{20}{35} times 15)

Solving this equation will give us the exact height of the smaller refrigerator.

Practical Considerations

While the mathematical solution is straightforward, practical considerations need to be taken into account. A refrigerator with a height of 15 meters (approximately 5 stories tall) would be impractical. Such a refrigerator would be extremely tall, leading to various logistical and operational challenges. It's highly likely that the original question might have a decimal point typo, making the height closer to 1.5 meters or 150 cm, which is a more reasonable size for a domestic refrigerator.

For those working with refrigerators, it's essential to consider the practicality of the dimensions in addition to the theoretical calculations. The suitability of a refrigerator for a given space is a critical factor in its design and installation.

Conclusion

In conclusion, while the problem presented offers a clear example of how to use volume and weight ratios to determine the height of a smaller refrigerator given its larger, similar counterpart, practical considerations should always be factored in. Always ensure that your design meets both functional and space requirements.