Current location - Training Enrollment Network - Mathematics courses - What are the knowledge points of six mathematical cylinders and cones?
What are the knowledge points of six mathematical cylinders and cones?
I. Similarities:

1, cylinders and cones have curved surfaces.

2. Both cylinders and cones have bottoms.

3. They are all drawings obtained by stretching a plan along a straight line that is not parallel to this plane.

Second, the difference:

(1), the side development diagram of the cylinder is rectangular (or square), the normal section is also rectangular (or square), and the upper and lower bottom surfaces are equal.

(2) The side of the cone is fan-shaped and the normal section is triangular. When the upper bottom surface of a cylinder shrinks to a point, it becomes a cone.

2. Bottom surface:

(1), the cylinder is also the bottom.

(2) Above the cone is a vertex.

3. Vertex:

(1), the cone has a vertex;

(2) A cylinder has no vertex.

Extended data:

A, cone composition:

1, the height of the cone: the shortest distance from the apex of the cone to the center of the bottom of the cone is called the height of the cone; ?

2. Cone generatrix: the radius of the sector formed by the expansion of the cone side and the distance from any point to the vertex on the circumference of the bottom surface.

3. Side area of the cone: the side of the cone is spread along the generatrix and is a fan. The arc length of this sector is equal to the circumference of the cone bottom, and the radius of the sector is equal to the length of the cone generatrix. The lateral area of the cone is arc length, and the circumference of the cone bottom × bus/2; It is a surface when it is not expanded.

4. A cone has a bottom surface, a side surface, a vertex, a height and numerous generatrix. The development diagram of the bottom surface is circular, and the development diagram of the side surface is fan-shaped.

Second, the nature:

1. The two circular surfaces of a cylinder are called the bottom surface, and the surrounding surfaces are called the side surfaces. A cylinder consists of two bottom surfaces and one side surface.

2. The two bottom surfaces of a cylinder are two identical circular surfaces. The distance between the two bottom surfaces is the height of the cylinder.

3. The side surface of the cylinder is a curved surface, and the development diagram of the side surface of the cylinder is a rectangle, a square or a parallelogram (diagonal cutting).

4. Transverse area of cylinder = bottom circumference x height.