Contents
In this publication, we will consider formulas that can be used to calculate the area of a sector of a circle, as well as analyze examples of solving problems to demonstrate their practical application.
Definition of a sector of a circle
Circle sector is the part formed by its two radii and the arc between them. In the figure below, the sector is shaded in green.
- AB – sector arc;
- R (or r) is the radius of the circle;
- α is the angle of the sector, i.e. angle between two radii. It is also sometimes called the central angle.
Formulas for finding the area of a sector of a circle
Through the length of the arc and the radius of the circle
Area (S) of a sector of a circle is equal to one second of the product of the arc length of the sector (L) and radius of the circle (r).
Through the angle of the sector (in degrees) and the radius of the circle
Area (S) of a sector of a circle equals the area of the circle multiplied by the angle of the sector in degrees (a°) and divided by 360°.
Through the angle of the sector (in radians) and the radius of the circle
Area (S) of a sector of a circle is equal to half the product of the angle of the sector in radians (aglad) and the square of the radius of the circle.
Examples of tasks
Task 1
A circle with a radius of 6 cm is given. Find the area of a sector if it is known that the length of its arc is 15 cm.
Solution
Let’s use the first formula, substituting the given values into it:
Task 2
Find the angle of a sector if its area is known to be 78 cm2, and the radius of the circle is 8 cm.
Solution
We derive a formula for finding the central angle from the second formula discussed above:
