Question

Вася вынес на улицу прямоугольный аквариум размером 40 см × 20 см × 25 см и доверху наполнил его снегом. Когда Вася вернулся домой, снег растаял, и оказалось, что объём получившейся воды равен 2 литрам. Во сколько раз плотность воды больше плотности снега?

Answer 1

Problem Analysis

Vasya placed a rectangular aquarium measuring 40 cm × 20 cm × 25 cm outside and filled it with snow. When he returned home, the snow had melted, and it was found that the volume of the resulting water was 2 liters. We need to determine the ratio of the density of water to the density of snow.

Solution

To find the ratio of the density of water to the density of snow, we need to calculate the densities of both substances and then divide the density of water by the density of snow.

Density of Water

The density of water is a well-known value. At room temperature (approximately 20°C), the density of water is about 1 gram per cubic centimeter (g/cm³) or 1000 kilograms per cubic meter (kg/m³) [[1]].

Density of Snow

The density of snow can vary depending on various factors such as temperature, moisture content, and crystal structure. On average, freshly fallen snow has a density of about 0.1 to 0.3 g/cm³ [[2]].

Calculating the Ratio

To find the ratio of the density of water to the density of snow, we can use the following formula:

Ratio = Density of Water / Density of Snow

Let's calculate the ratio using the given values:

Density of Water = 1000 g/cm³ Density of Snow = 0.1 - 0.3 g/cm³ (average value)

Ratio = 1000 g/cm³ / 0.1 - 0.3 g/cm³

Since the density of snow can vary, we'll calculate the ratio using the minimum and maximum values:

Minimum Ratio = 1000 g/cm³ / 0.3 g/cm³ Maximum Ratio = 1000 g/cm³ / 0.1 g/cm³

Calculating the minimum and maximum ratios:

Minimum Ratio = 3333.33 Maximum Ratio = 10000

Therefore, the density of water is approximately 3333.33 to 10000 times greater than the density of snow.

Conclusion

The density of water is significantly greater than the density of snow. The ratio of the density of water to the density of snow is approximately 3333.33 to 10000.