Question

В цилиндрическом сосуде с тонкими вертикальными стенками высотой Н=7 см. находится некоторый объём воды.V В сосуд опустили медный кубик массой 445 г. При этом кубик оказался полностью погруженным в воду, а вода не вылилась из сосуда и поднялась до его верхнего края. Определите объём воды в сосуде, площадь дна сосуда 50 см(2), плотность меди 8, 9 г\см(3)

Answer 1

найдем весь объём цилиндра V=SH=0,005м2 * 0,07=0,00035м3

найдём объём кубика из формулы V=m/р(плотность)=0.445/ 8900=0,00005м3

найдём первоначальный объём воды:   0,00035м3- 0,00005м3=0,0003м3 или 300см3

Answer 2

Problem Analysis

We are given a cylindrical vessel with thin vertical walls and a height of 7 cm. The vessel contains a certain volume of water. A copper cube with a mass of 445 g is submerged in the vessel, causing the water to rise to the top without overflowing. We need to determine the volume of water in the vessel.

Solution

To solve this problem, we can use the principle of buoyancy. According to Archimedes' principle, the buoyant force acting on an object submerged in a fluid 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

The weight of the fluid displaced is equal to the weight of the water that has risen in the vessel. We can calculate the weight of the water using the formula:

Weight of water = Density of water * Volume of water * g

where: - Density of water = 1 g/cm³ (approximately) - Volume of water is the volume we need to find - g is the acceleration due to gravity, which is approximately 9.8 m/s²

Since the density of water is approximately equal to 1 g/cm³, we can assume that the volume of water displaced is equal to the volume of the copper cube. Therefore, we can calculate the volume of water using the formula:

Volume of water = Mass of copper cube / Density of copper

where: - Mass of copper cube = 445 g - Density of copper = 8.9 g/cm³ (approximately)

Let's calculate the volume of water using the given values.

Calculation

Given: - Height of the vessel (H) = 7 cm - Mass of the copper cube (m) = 445 g - Density of copper = 8.9 g/cm³

We need to find the volume of water in the vessel.

Using the formula: Volume of water = Mass of copper cube / Density of copper

Substituting the values: Volume of water = 445 g / 8.9 g/cm³

Converting the units: Volume of water = 445 cm³ / 8.9 cm³/g

Simplifying: Volume of water = 50 cm³

Therefore, the volume of water in the vessel is 50 cm³.

Answer

The volume of water in the cylindrical vessel is 50 cm³.

Note: The sources used for this response are and