Key parameters which measure a circle are its radius, the area and length of a circle. To find some share - for example, two thirds - from each of these sizes are possible by the simplest calculations. But sometimes there is a need to allocate on the drawn circle "segment", size in the same two thirds of its area. Such share of a circle is usually called the sector - it is formed by two radiuses and an arch of a circle. It is possible to allocate such sector in general without any calculations.
It is required to you
- Paper, compasses, protractor, ruler.
Instruction
1. If at your disposal there are a drawn circle and compasses, it will be simple to allocate two thirds in this drawing. Postpone the radius of a circle on compasses and establish a needle in any point of a circle, i.e. circle border. Make marks in a circle in both parties from the point chosen on it. These two marks divide the line limiting a circle into two arches. Length bigger of them is equal to two thirds of length of perimeter, so the task is solved. You can draw the straight lines connecting these points to the center if in conditions it is required to draw the sector with the size in two thirds of a circle.
2. The compasses can be replaced with a protractor and a ruler. In this case at first put the end to any place of a circle - it will be one of the borders dividing two arches. Then apply a protractor to the straight line passing through this point and the center of a circle so that the zero mark coincided with the center of a figure. Put the auxiliary end opposite to a mark to 120 °. Then by means of a ruler note crossing with a circle of the beam beginning in the center of a circle and passing through an auxiliary point. This crossing will be the second border dividing two arches - big of them will be equal to two thirds of a circle. It will be necessary only to carry out two radiuses if it is necessary to draw the sector on the drawing.
3. If necessary not to draw but only to calculate the size (l) equal to two thirds of length of a circle, it is necessary to know diameter of a circle (D). Length of all border of this figure is equal to the work of diameter on Pi's number therefore for receiving the answer multiply this size by two thirds: l = ⅔*π*D.
4. For calculation of the area of the sector (s) equal to two thirds of a circle, it is more convenient to use instead of diameter its half - the radius (R). The area of all circle is equal to the work of the same number of Pi on the radius squared. For calculation of the area of the necessary segment find two thirds of this size: s = ⅔*π*R².