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## Area of a Sector

Area of a Sector can be obtained by multiplying the circle’s area by the ratio of the angle and 2π (because the area of the sector is proportional to its angle, and 2π is the angle for the whole circle, in radians).

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A circular sector or circle sector (symbol: ⌔), is the portion of a disk enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger being the major sector.

### Area of a Sector

Sector: A region bounded by two radii and an arc of a circle (plain English definition: The shape of a piece of pizza)

Segment Of A Circle: A region bounded by a chord and an arc of a circle

Formula to Calculate Area, Perimeter, Circumference: Find Area of Circle

Area of Sector Formula

Area of a Sector (such as sector PQR in the above figure) is equal to the area of the circle is (πr2)

Times the fraction of the circle represented by the sector:

Let θ be the central angle, in radians, and r the radius. The total area of a circle is πr2. The area of the sector can be obtained by multiplying the circle’s area by the ratio of the angle and 2π because the area of the sector is proportional to the angle, and 2π is the angle for the whole circle):

A= πr2 ∙ (θ/2π) = (θ/2) r2 = (1/2) r2θ

Also, if θ refers to the central angle in degrees, a similar formula can be derived.

A= πr2 · (Θ/360)

Sectors can have special relationships, which include halves, quadrants, and octants.

The length L of the arc of a sector is given by the following formula:

L=π · (θ/180) r

Where θ is in degrees

The length of the perimeter of a sector is sum of arc length and the two radii. It is given by the following formula:

L= {2+ π · (θ/180)} r

Where θ is in degrees

The sector area of a Polygon is:

How To Find Area Of Right Angled Triangle: Formula with Examples

Perimeter of Sector

The length of the perimeter of a sector is the sum of the arc length and the two radii:

P= l+2r= θ+2r=r (θ+2)

Area of Sector and Arc Length

Formula for Arc Length

S=r θ

Where, S represents the arc length, r represents the radius of the circle and θ represents the angle in radians made by the arc at the centre of the circle.

How to Find the Area of a Sector

Question) A circular, 8-slice pizza is placed in a square box that has dimensions four inches larger than the diameter of the pizza. If the box covers a surface area of 256 in2, what is the surface area of one piece of pizza?

Explanation:

The first thing to do is calculate the dimensions of the pizza box. Based on our data, we know 256 = s2. Solving for s (by taking the square root of both sides), we get 16 = s (or s = 16).

Now, we know that the diameter of the pizza is four inches less than 16 inches. That is, it is 12 inches. Be careful! The area of the circle is given in terms of radius, which is half the diameter, or 6 inches. Therefore, the area of the pizza is π * 62 = 36π in2. If the pizza is 8-slices, one slice is equal to 1/8 of the total pizza or (36π)/8 = 4.5π in2.

Want to Know? How to Find Area of Square

Question) If B is a circle with line AC = 12 and line BC = 16, then what is the area formed by DBE?

Explanation:

Line AB is a radius of Circle B, which can be found using the Pythagorean Theorem:

AB2=AC2+BC2→AB=√AC2+BC2=√162+122=√400=20
Since AB is a radius of B, we can find the area of circle B via:
Area=πR2=π(202)=400π
Angle DBE is a right angle, and therefore 1/4 of the circle so it follows:
Area(DBE)=400/4π=100π

Get Maths Vedic/Basic Formulas Free List: Maths Formulas

Question) The radius of the circle above is 4 and ∠A=45∘.  What is the area of the shaded section of the circle?

Explanation:

Area of Circle = πr2 = π42 = 16π
Total degrees in a circle = 360
Therefore 45 degree slice = 45/360 fraction of circle = 1/8
Shaded Area = 1/8 * Total Area = 1/8 * 16π = 2π

Question) PQ is the arc of a circle with center O. If the area of the sector is 3π what is the perimeter of sector?

Explanation:

First, we figure out what fraction of the circle is contained in sector OPQ: 300/3600=112, so the total area of the circle is 12*3 π=36

Using the formula for the area of a circle, πr2 πr2, we can see that r=6
We can use this to solve for the circumference of the circle, 2πr, or 12π.
Now, OP and OQ are both equal to r, and PQ is equal to 1/12 of the circumference of the circle, or π.
To get the perimeter, we add OP + OQ + PQ, which give us 12+π.

Want to Know? How to Find Area of Quadrilateral

Area Of A Sector Formula Calculator

The online Area of A Sector Calculator is used to help you find the area of a sector of a circle. The calculator is not hard to use.

Follow the below mentioned instructions to use area of a sector calculator:

• Enter the length of the radius of the circle
• Enter the measure of the angle between the radii
• Then hit on the button that says calculate
• Do not enter numbers with a slash (/)! If you do, the wrong answer will be computed
• Therefore, convert all fractions into decimals before entering numbers
• Enter all numbers without the unit. For example, if r = 5 cm, enter 5.
• For the angle, enter a positive number smaller or equal to 360

Must Read: How to Prepare for Maths

Final Words:

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