At rotation of a rectangular triangle around one of its legs the rotation figure called a cone is formed. A cone — a solid with one top and the round basis.
Instruction
1. Arrange the drawing square, having combined one of legs with the table plane. Without tearing off side of the square from a surface of a table turn the square around the second leg. Keep vertical position of the drawing tool at its rotation that the top of the square remained motionless.
2. After a whole revolution the top of the square will outline the circle limiting the basis of the received rotation body on a table. The top of a right angle will remain in the center of the round basis with a radius equal to the leg lying on the table plane. The leg which served as a rotation axis becomes height of an educated cone. The top of a cone is located precisely over the center of a circle in the basis. The hypotenuse of the square is forming a cone.
3. Axial section belongs to the plane in which the cone axis is located. It is obvious that the plane of axial section is perpendicular to the basis of a cone and cuts a cone on two equal parts. The figure which turned out in the plane of axial section — an isosceles triangle. The basis of this triangle is equal to diameter of a circle of the basis of a cone, sides are equal forming a cone.
4. Height of an isosceles triangle in the plane of axial section lowered on the basis is equal to height of a cone and at the same time is a symmetry axis. The axis of symmetry divides a figure of axial section into two equal rectangular triangles. Legs of these rectangular triangles — circle radius in the basis of a cone and cone height. Hypotenuses of the received rectangular triangles are equal forming a cone.
5. The area of an isosceles triangle is equal to a half of the work of diameter of the basis of a cone on cone height in the section of a cone. The area S rectangular triangles is equal in axial section to a half of the area of full section and can be calculated on a formula: S = d*h/4 where d is diameter of the basis, h is cone height.