The term "sector" can have several meanings. In geometry and some other sciences, this is a part of a circle bounded by two radii, an angle between them and an arc of this angle. In everyday life, it can also be an object that exists in reality and has an appropriate shape. Its area is calculated in the same way as the area of the geometric sector. Such calculations may be required, for example, in the manufacture of furniture, curly windows and stained-glass windows.
Necessary
- - a circle of a given radius;
- - sector angle.
- - drawing accessories.
Instructions
Step 1
Construct a circle with a given diameter. If you need to calculate the area of a real object that has the appropriate shape, take the necessary measurements. In the same way as for solving a school problem in geometry, you need a radius and an angle. A protractor may not always be at hand, so you can measure the length of the arc in any available way, and use it to calculate the angle. For the convenience of calculations, you can also make a drawing.
Step 2
Separate the sector from the resulting circle by drawing 2 radii. To solve a school problem, it is not necessary to accurately measure the angle, draw a conditional sector with conditional dimensions. If necessary, it will be possible to make an accurate drawing based on the data received.
Step 3
Most likely, in the conditions of the problem, the size of the angle is given in degrees. You need to convert it to radians. It is equal to the angle in degrees multiplied by the factor π and divided by 180 °. It can be found by the formula Ap = Ar * n / 180 °, where Ar is the size of the angle in degrees, Ap is in radians.
Step 4
Calculate the area of the sector. It is equal to the size of the angle in radians multiplied by the square of the radius and divided by 2. That is, S = (Ap * r2) / 2.
Step 5
To build a pattern and other practical purposes, you may need to calculate the arc length of a sector. This can also be done through the angle size, expressed in radians. The arc length of the sector is equal to the angle multiplied by the radius. This parameter can be expressed by the formula L = Ap * r.
