Circular sector is a very special geometric form in plane geometry. The following article introduces to you the concept of what a sector is, the formula for calculating the area of a circular sector, and the circumference of a circular sector. Please refer to it.
Round fan shape
The shape bounded by two radii OA, OB and circular arc AB as shown below is called a circular sector.
So a sector is a part of a circle bounded by two radii and an arc.
Let S be the area of a circular sector, then the formula for calculating the area of a circular sector has 2 expressions:
or
In there:
Sis the area of a circular sectorRis the radius of the circle, as in the picture then R = OA = OBℓis the arc length, according to the figure, ℓ has the same length as arc AB.The formula for calculating the perimeter of a circular sector is determined by the formula:
In there:
Cis the circumference of the fanRis the radius of the circle with center Oℓis the arc lengthLesson 1 :
Calculate the area of a circular sector when radius R = 5 cm, angle n = 30º.
Solution : Applying the formula for calculating the area of a fan, we have:
Lesson 2 :
Calculate the area of a circular sector when knowing the radius R = 7 cm, arc length ℓ = 5 cm.
Solution : Applying the formula for calculating the area of a fan, we have:
Lesson 3:
Calculate the perimeter of a sector with area 8 cm2 and arc length 5 cm.
Solution : We have:
Based on the formula for calculating the perimeter of a fan, we have: C = 2R + ℓ = 2.3.2 + 5 = 11.4 (cm).
Also don't miss the series of articles on calculating the area of a circle , the area of a pyramid and a series of other shapes.
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