Elementary school Olympiad changes in water surface height

1.The length, width and height of the goldfish bowl are 50 cm, 24 cm and 40 cm respectively, if you put liters of water in it, how many cm is the water surface from the mouth of the tank? liter = cubic decimeter = 38400 cubic centimeter 38400 (50 24) = 38400 1200 = 32 (cm) 42-32 = 8 (cm) 2

A cuboid container with a base of a square with a side length of 60 cm. Inside the container stands a rectangular piece of iron 1 meter high and 15 centimeters long on the side of the ground, which is the depth of water in the container. Now gently lift the piece of iron up 24 centimeters, how many centimeters is the water-soaked part of the piece of iron that is exposed to the water?

15 15 24 (60 60) + 24 = 5400 3600 + 24 = = cm).

Question 1: Convert the component meters to find that the bottom area of the fish tank is 5 with cubic decimeters, and the water surface height is the water surface away from the fish tank. The second question is too lazy to forget it.

Question 1: liter = cubic decimeter = 38400 cubic centimeter 42- 38400 (50 24) = 38400 1200 = 8 (centimeter) Question 2: 15 15 24 (60 60) + 24 = centimeter).

Example 1 A cylindrical container containing water has an inner radius of 5 cm, a depth of 20 cm, and a depth of 15 cm. Now put an iron cylinder with a bottom radius of 2 cm and a height of 17 cm vertically into the container, find out how many centimeters of water depth of the container at this time?

Solution: After putting in the iron cylinder, if the iron cylinder is high enough, then the water depth = (5 5 15) (5 5 -2 2 ) = 17 and 6 7 cm.

Because 17 and 6 7 > 17, the iron cylinder is completely submerged in water, so the water depth should be 15 + (2 2 17) (5 5 ) = cm.

Example 2A cylindrical container containing water with an inner radius of 5 cm on the bottom surface, 20 cm deep and 15 cm deep. Now put an iron cylinder with a bottom radius of 2 cm and a height of 18 cm vertically into the container, find out how many centimeters of water depth of the container at this time?

Solution: After putting in the iron cylinder, if the iron cylinder is high enough, then the water depth = (5 5 15) (5 5 -2 2 ) = 17 and 6 7 cm.

Because 17 and 6 7 < 18, the iron cylinder is only partially submerged in the water, and is still partially exposed. So the depth of the water should be (5 5 15) (5 5 -2 2 ) = 17 and 6 7 cm.

Question: Carefully observe the calculation process of finding the water depth after putting the iron container in the two questions, why only the height of the iron cylinder is changed in the two questions, why is the calculation process of the water depth different?

Analysis: To solve this kind of problem, the first thing to do is to determine whether the object you put in is completely submerged in water. The key to solving the problem is to grasp that the volume of water does not change, but only the shape of water.

In Example 1, the iron cylinder is completely submerged in water, so that the water expelled by the iron cylinder is in the shape of a cylinder with a base radius of 5 cm. In Example 2, the iron cylinder is only partially submerged in water and is still partially exposed, at this time, the shape of the water extruded by the cylinder is a hollow cylinder, and the bottom area of the water is the difference between the bottom area of the container and the bottom area of the iron cylinder.

Is it a liquid pressure problem?

You can buy a middle school physics competition book that has what you want.

If you are in the sixth grade of primary school, go and watch "Gold Medal Olympiad".