How to Draw Sector of a Circle
A circle has ever been an important shape amidst all geometrical figures. In that location are various concepts and formulas related to a circle. The sectors and segments are maybe the most useful of them. In this article, we shall focus on the concept of a sector of a circumvolve along with area and perimeter of a sector.
A sector is said to be a part of a circle made of the arc of the circumvolve forth with its two radii. Information technology is a portion of the circumvolve formed by a portion of the circumference (arc) and radii of the circle at both endpoints of the arc. The shape of a sector of a circumvolve can be compared with a piece of pizza or a pie. Earlier we start learning more than about the sector, offset let the states learn some basics of the circle.
- Area Of Sector Of A Circle
- Surface area of a Sector of Circle Formula
- Area of a Segment of a Circle Formula
- Segment and Areas of Segment of a Circle
- Parts of a Circle
What is a Circle?
A circle is a locus of points equidistant from a given point located at the centre of the circle. The common distance from the centre of the circle to its point is called the radius. Thus, the circumvolve is defined by its center (o) and radius (r). A circle is also divers by two of its properties, such as expanse and perimeter. The formulas for both the measures of the circumvolve are given by;
-
- Expanse of a circumvolve = πr2
- The perimeter of a circumvolve = 2πr
What is Sector of a circle?
The sector is basically a portion of a circle which could be defined based on these three points mentioned below:
- A circular sector is the portion of a deejay enclosed past 2 radii and an arc.
- A sector divides the circumvolve into two regions, namely Major and Small Sector.
- The smaller expanse is known as the Modest Sector, whereas the region having a greater area is known every bit Major Sector.
Area of a sector
In a circle with radius r and centre at O, permit ∠POQ = θ (in degrees) be the bending of the sector. And so, the surface area of a sector of circle formula is calculated using the unitary method.
For the given bending the area of a sector is represented past:
The angle of the sector is 360°, area of the sector, i.e. the Whole circle = πr2
When the Bending is ane°, area of sector = πrtwo /360°
And then, when the angle is θ, area of sector, OPAQ, is defined as;
Allow the angle exist 45 °. Therefore the circle volition be divided into viii parts, as per the given in the below effigy;
Now the expanse of the sector for the above figure can be calculated as (i/8) (3.14×r×r).
Thus the Area of a sector is calculated as:
Length of the Arc of Sector Formula
Similarly, the length of the arc (PQ) of the sector with angle θ, is given by;
l = (θ/360) × 2πr (or)l = (θπr) /180
Area of Sector with respect to Length of the Arc
If the length of the arc of the sector is given instead of the angle of the sector, there is a different mode to calculate the area of the sector. Let the length of the arc be l. For the radius of a circle equal to r units, an arc of length r units volition subtend 1 radian at the centre. Hence, it can be ended that an arc of length l will subtend l/r, the angle at the centre. So, if l is the length of the arc, r is the radius of the circumvolve and θ is the angle subtended at the heart, then;
θ = 50/r, where θ is in radians.
When the angle of the sector is 2π, then the area of the sector (whole sector) is πr2
When the bending is one, the area of the sector = πr2 / 2π= r2 /2
So, when the angle is θ, area of the sector = θ × rtwo/ii
A = ( l/r) × (r2/two)
Some examples for better understanding are discussed here.
Examples
Case one: If the bending of the sector with radius iv units is 45°, then find the length of the sector.
Solution: Area = (θ/360°) × πrii
= (45°/360°) × (22/7) × four × 4
= 44/7 square units
The length of the same sector = (θ/360°) × 2πr
l = (45°/360°) × 2 × (22/7) × 4
l = 22/seven
Case 2: Discover the area of the sector when the radius of the circle is xvi units, and the length of the arc is 5 units.
Solution: If the length of the arc of a circle with radius 16 units is five units, the expanse of the sector corresponding to that arc is;
A = (lr )/2 = (5 × sixteen)/ii = 40 square units.
Perimeter of a Sector
The perimeter of the sector of a circle is the length of two radii along with the arc that makes the sector. In the following diagram, a sector is shown in xanthous color.
The perimeter should exist calculated by doubling the radius and and then calculation it to the length of the arc.
Perimeter of a Sector Formula
The formula for the perimeter of the sector of a circle is given below :
Perimeter of sector = radius + radius + arc length
Perimeter of sector = two radius + arc length
Arc length is calculated using the relation :
Arc length = 50 = (θ/360) × 2πr
Therefore,
Perimeter of a Sector = 2 Radius + ( (θ/360) × 2πr)
Example
A round arc whose radius is 12 cm, makes an angle of 30° at the centre. Find the perimeter of the sector formed. Use π = 3.xiv.
Solution : Given that r = 12 cm,
θ = 30° = 30° × (π/180°) = π/6
Perimeter of sector is given by the formula;
P = two r + r θ
P = 2 (12) + 12 ( π/6)
P = 24 + ii π
P = 24 + 6.28 = 30.28
Hence, Perimeter of sector is xxx.28 cm
Source: https://byjus.com/maths/sector-of-a-circle/
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