Question

в сосуд с водой поместили кубик льда,а сверху на него поставили кубик из алюминия, при этом верхняя грань кубика льда сравнялась с уровнем воды в сосуде. в кубик льда имеется полость с воздухом. после того как лёд растаял в алюминиевый кубик опустился на дно сосуда,уровень воды в сосуд понизился на 10 см. определите объем алюминиевого сосуда 0,85 м2, плотность воды 1000кг/м3, плотность алюминия 2700 кг/м3. весом воздуха в полости пренебречь ​

Answer 1

Ответ:0,05м2

Объяснение

Answer 2

Problem Analysis

We have a scenario where a cube of ice is placed in a vessel filled with water. On top of the ice cube, an aluminum cube is placed. The top surface of the ice cube is at the same level as the water in the vessel. After the ice cube melts, the aluminum cube sinks to the bottom of the vessel, causing the water level to decrease by 10 cm. We need to determine the volume of the aluminum cube.

Solution

To solve this problem, we can use the principle of buoyancy. When an object is submerged in a fluid, it experiences an upward force called buoyant force, which is equal to the weight of the fluid displaced by the object. The buoyant force can be calculated using the formula:

Buoyant force = Weight of the fluid displaced = Density of the fluid × Volume of the fluid displaced × g

where: - Density of the fluid is the density of water (1000 kg/m^3). - Volume of the fluid displaced is the volume of the ice cube that melted. - g is the acceleration due to gravity (approximately 9.8 m/s^2).

Since the aluminum cube sinks to the bottom of the vessel after the ice cube melts, the volume of the aluminum cube is equal to the volume of the ice cube that melted.

To find the volume of the ice cube that melted, we can use the fact that the water level in the vessel decreased by 10 cm. The volume of the water that was displaced by the aluminum cube is equal to the volume of the aluminum cube. Therefore, we can calculate the volume of the aluminum cube using the formula:

Volume of the aluminum cube = Volume of the water displaced = Cross-sectional area of the vessel × Change in water level

To find the cross-sectional area of the vessel, we need to know the dimensions of the vessel. However, the dimensions of the vessel are not provided in the question. Therefore, we cannot determine the exact volume of the aluminum cube without this information.

Conclusion

In conclusion, we cannot determine the volume of the aluminum cube without knowing the dimensions of the vessel. The information provided in the question is insufficient to solve the problem.