The cone represents a solid, obrazuyushcheesya at rotation of a triangle. pryamy the cone turns out from a rectangular triangle, kotory rotate around one of legs. to razvernut a cone on the plane means to construct its development. it is possible to sdelat it as on the sheet of paper by means of compasses and a ruler, tak and on the computer screen. naprimer, v to the AutoCAD program.
It is required to you
- - konus ;
- - list of paper ;
- - tsirkul ;
- - lineyka ;
- - transportir ;
- - kalkulyator ;
- - a computer with the AutoCAD program.
Instruction
1. To construct development, neobkhodimo to know cone parameters. esl it is a solid exists in reality, to its izmerta. dlya solutions of a task from the textbook draw a projection of a conditional cone. the ona represents an isosceles triangle, the osnovaniye of which is equal to diameter of the basis of a cone.
2. Carry out necessary calculations. the razvertka of a side surface represents the sector, a dlin of an arch of L whom it is equal to basis circle length. to its vychislita on formula L = 2πг, to r gda – radius the bases. dlya creation of development to you it has to be also known forming a cone, kotory at the same time is also R arch radius. ugol sectors it is equal to a ratio of radiuses of the circle lying in the basis and sectors, umnozhenny on 360º.
3. To develop a side surface of a cone on the plane by means of classical drawing tools, to a postroyta a circle with R radius. you provedit one radius. a otlozhit from it a corner of the sector and through the received point carry out one more radius. et two pieces together with prisoners between them a corner and an arch also represent development of a side surface of a cone.
4. To develop a cone on the plane in AutoCAD, draw at first an isosceles triangle which basis is equal to diameter of the basis of a cone, and side - forming. Take one of points of intersection of the basis and side for the center of a circle which radius R is equal to triangle side. v to the program creation of a circle in different parameters is provided, v this case it is the most convenient on the center and radius.
5. Carry out through 2 tochka of the turned-out circle any straight line. u you it has to turn out 2 dug. to a luchsha to make them different in the size. Cut one part and remove the line.
6. chtoba to find the corner size, find the built-in calculator. It is in the main menu, in the svoystvo tab . the Program will suggest you to specify initial and final corners. Final calculate on the same formula, as for the "paper" drawing, that is enter the sizes of radiuses and increase what at you turned out at division, on 360º. You on the screen have to have a sector which parameters correspond to cone parameters.
7. chtoba to construct full development, you need still the drawing of the basis. It represents a circle which radius is known to you. If you develop a cone on the plane by means of a ruler and compasses, draw a circle so that it in one of points concerned an arch. In the AutoCAD program it is convenient to use the basis of already nacherchenny triangle as diameter. Then it is possible to transfer a circle to the necessary part of the drawing.