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How can we find the area of a sector of a circle?
The circles are very important and interesting shapes that are used for various purposes. They have many interesting properties which we must study in order to get our concepts cleared. The sector of a circle is a part of the circle formed by two radii and an arc of a certain length. Imagine pizza slices to get a better idea!
Answer: The area of a sector of a circle is given by θ°/360° × πr², where θ° is the angle formed by the sector and r is the radius of the circle.
Let us understand the answer in detail.
We know that the area of a circle is πr2. To find the area of a sector of a circle, we use the concept of angles.
Let's take the example of a semi-circle.
We know it has an area that is half of a complete circle, that is, πr2/2.
Now, we know that the radii subtend an angle of 180 degrees at the center in a semi-circle.
Hence, it can be written as 180°/360° × πr2 which is equal to the result above.
Similarly, we can prove the area of the quarter of a circle as well.
Hence, The area of a sector of a circle is given by θ°/360° × πr2, where θ° is the angle formed by the sector.