The two circular surfaces of a cylinder are called the bottom surface and the curved surface is called the side surface. The distance between two bottoms is called height. A cylinder has countless heights, all of which are equal in length. The bottom of the cone is a circular surface, and the side of the cone is a curved surface. The distance from the apex of the cone to the center of the bottom surface is the height of the cone, and there is only one height of the cone.
After the cylinder is unfolded, we can find that the side of the cylinder is a rectangle, the length of one side of the rectangle is equal to the circumference of the bottom of the cylinder, and the length of the other side is equal to the height of the cylinder, so the lateral area of the cylinder = the circumference of the bottom × the height. The lateral area of a cylinder plus two bottom areas is the surface area of the cylinder, that is, the surface area =2πr×h+2πr? .
Converting the volume of a cone into the volume of a cylinder also uses the idea of transformation, which is one of the most commonly used ideas in primary school mathematics. Through research, we find that the volume of a cone is equal to one-third of the volume of a cylinder with the same height as its bottom. Then the volume formula of the cone: V= 1/3sh= 1/3πr? h .
Understanding of cylinders and cones;
There is a fixed line and a moving line in the same plane. When a plane rotates once around a fixed line, the surface formed by the moving line is called the rotating surface, the fixed line is called the axis of the rotating surface, and the moving line is called the generatrix of the rotating surface. If the generatrix is a straight line parallel to the axis, then the generated surface of revolution is called a cylindrical surface.
If two planes perpendicular to the axis are used to cut the cylindrical surface, then the geometry surrounded by these two sections and the cylindrical surface is called a straight cylinder, which is called cylinder for short.
A cone is a geometric figure with two definitions. Analytic geometry definition: A spatial geometry consisting of a conical surface and a plane intersecting it (satisfying that the intersection line is a circle) is called a cone. Definition of solid geometry: The geometry formed by taking the straight line where the right side of a right triangle is located as the rotation axis and the other two sides rotating 360 degrees is called a cone.