Mathematical column handwritten newspaper
Definition of cylinder: The revolving body surrounded by the straight line where one side of a rectangle is located is called the surface area of the cylinder =2× bottom area+lateral area cylinder. The expanded side is square or rectangle, and the length of the expanded side is the perimeter of the bottom surface, and the width is high (the perimeter of the bottom surface is square when it is equal to the height, so the special case of the side surface expanding along the height is square), so the lateral area is equal to the perimeter of the bottom surface× height. The distance between the two bottom surfaces is called the height of the cylinder. A cylinder has countless heights, all of which are of equal length. Finding the volume of a cylinder is the same as finding the volume of a cuboid or cube, and it is the bottom area× height: if the radius of the bottom surface of the cylinder is R and the height is H, then the volume V: V = π r 2h, if S is the bottom area, the height is H, and the volume V: V = SH, and the lateral area of the cylinder = the perimeter of the bottom surface * the two circular surfaces of the high cylinder are called the bottom surface (divided into the upper bottom and the lower bottom); A cylinder has a curved surface called a side surface; The distance between two bottom surfaces is called height (there are countless heights). Cone: The spatial geometry consisting of a conical surface and a plane intersecting it (the intersection line is a circle) is called a cone. The volume of a cone is equal to 1/3 the volume of a cylinder with the same height as the bottom surface. According to the cylinder volume formula V=Sh(V=rrπh), the cone volume formula is obtained: cone V= 1/3Sh The surface area of a cone is called the surface area of this cone. The surface area of a cone consists of the side area and the bottom area. Height of the cone: the distance from the apex of the cone to the center of the bottom of the cone is called the height of the cone; Lateral area of the cone: The side of the cone spreads along the generatrix and is a sector. 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. Lateral area of the cone is arc length and circumference of the cone bottom * generatrix/2; It is a surface when it is not expanded. The generatrix of the cone: the radius of the sector formed by the expansion of the side of the cone, and the distance from the point on the circumference of the bottom surface to the vertex. A cone has a bottom surface, a side surface, a vertex, a height and countless generatrixes, and the side surface development diagram is fan-shaped. The lateral expansion of the cone is a sector, and the known sector area is 1/2rl. Therefore, the lateral area of the cone is 1/2 bus length × arc length (that is, the perimeter of the bottom surface). In addition, the cone whose generatrix length is equal to the diameter of the bottom circle is a semicircle. After the answer, you can filter according to your needs.