Cylindrical brother is the most common three-dimensional figure in our daily life. Such as tea barrels, cans and other items are cylindrical. The upper and lower surfaces of a cylinder, called the bottom surface, are two equal circles. A cylinder has countless heights, and each height is equal. It also has a general formula for calculating the volume of cubes and cuboids: v=sh.
Sister Tong is a "close relative" of Brother Tong. Why? Because its bottom is also round, but it has only one bottom. And the height is also one. The way to calculate a cone is to multiply its height by its base area, and then multiply it by "1/3". Because the volume of a cone is 1/3 of the volume of a cylinder with the same height as its bottom, we often miss the multiplication operation of "1/3" in calculation, so we should practice more. When we see the problem of finding the volume of a cone, we can conditionally think of multiplying it by "1/3".
Knowing this knowledge, I'm going to test you. There is a wooden cylinder that can be cut into three largest cones. Some students think this problem is right, but in fact, they can only cut 1 the largest cone, because the cut part is not a cone, but 2/3 of the cylinder volume. If you change the problem to 1 cylinder, you can cast three largest cones, that's right.
There are some connections between a cylinder and a cone. For example, when the heights of a cylinder and a cone are equal, the volume of the cylinder is three times that of the cone. (as shown in the figure below)
S=S
h=h
v=3: 1
When the cylinder and the cone have the same volume and the same bottom surface, the height of the cone is three times that of the cylinder (as shown in the figure below).
v=v
s=s
h= 1:3
When the volumes of cylinder and cone are equal, the area of cone is three times that of cylinder. (as shown in the figure below)
r=r
h=h
s= 1:3
Students, under my introduction, do you have any insights?