The cone represents a solid which basis represents a circle, and side surfaces are all pieces which are carried out from the point which is out of the basis plane to this basis. The direct cone which usually is considered in a school course of geometry can be presented as the body formed by rotation of a rectangular triangle around one of legs. Perpendicular section of a cone is the plane passing through its top is perpendicular to the basis.
It is required to you
- The drawing of a cone with the set parameters
- Ruler
- Pencil
- Mathematical formulas and definitions
- Cone height
- Cone basis circle radius
- Formula of the area of a triangle
Instruction
1. Draw a cone with the set parameters. Designate the center of a circle as Oh, and cone top — as P. You need to know the radius of the basis and height of a cone. Remember properties of height of a cone. It represents the perpendicular which is carried out from cone top to its basis. The cone height point of intersection with the basis plane at a direct cone coincides with the center of a circle of the basis. Construct the axial section of a cone. It is formed by diameter of the basis and forming a cone which pass through diameter points of intersection with a circle. Designate the received points as And yes Century.
2. Axial section is formed by two rectangular triangles which are lying in one plane and having one general leg. It is possible to calculate the area of axial section in two ways. The first way is to find the areas of the turned-out triangles and to put them together. It is the most evident way, but in fact it differs in nothing from classical calculation of the area of an isosceles triangle. So, at you 2 rectangular triangles which general leg is h cone height, the second legs — R basis circle radiuses, and hypotenuses — forming a cone turned out. As all three parties of these triangles are equal among themselves, and triangles turned out equal, according to the third property of equality of triangles too. The area of a rectangular triangle is equal to a half of the work of its legs, that is S=1/2Rh. The area of two triangles will be respectively equal to the work of radius of a circle of the basis on height, S=Rh.
3. Axial section is considered most often as an isosceles triangle which height is cone height. In this case it is a triangle of ARV which basis is equal to diameter of a circle of the basis of a cone of D, and height is equal to h cone height. The area it is calculated on a classical formula of the area of a triangle, that is as a result we receive the same formula S = 1/2Dh = Rh where S is the area of an isosceles triangle, R is basis circle radius, and h is the triangle height which is at the same time and cone height.