Formula Area of Sector

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We know that the area of a sector can be calculated using the following formulas Area of a Sector of Circle θ360º πr 2 where θ is the sector angle subtended by the arc at the center in degrees and r is the radius of the circle. Now that you know the value of θ and r you can substitute those values into the Sector Area Formula and solve as follows.


Area Of A Sector Of A Circle Proof Sectors Mathematics Areas Sector Of A Circle Mathematics Math

A θ360 πr 2.

. So whats the area for the sector of a circle. A sector θ 2 r 2. Area of a sector.

Area of a circular sector using radians. The area of a sector of a circle is the amount of space occupied inside a sector of a circles border. A circle with a radius of 100 cm has a sector making an angle of 60 at the center.

Area of a Sector. Note that α should be in radians. A sector always begins at the circles centre.

There are three formulas for calculating the area of a sector. The semi-circle is likewise a sector of a circle. The perimeter of a sector can be calculated if the area of the sector is given.

In a circle with radius r and centre at O let POQ θ in degrees be the angle of the sector. In this case a circle has two equal-sized sectors. Simplify the numerator then divide.

A complete circle has a total of 2π radians which is equal to 360. The formula used to calculate the area of a sector of. A sector θ 2 π π r 2.

A lighthouse casts a red-colored light over a sector of angle 70 to a distance of 20 km to warn sailors of undersea rocks. R2 equals 52 25 in this example. Angle of sector at center 60 Formula for area of a sector θ360πr 2.

Now since we know that the total measure of a circle is 360 degrees the area of the circle will be A 1 360 π r 2. Therefore we can modify the above formula to use it when we have the circular sector defined in radians. Find the area of the sector.

For the given angle the area of a sector is represented by. Area of the sector θ360 π r 2 20360 x 314 x 3 x 3 157. Sector Area α πr² 2π α r² 2.

So θ 63 and r 5. Replace r with 5. Lets study how to determine the area of a sector.

A sector θ 360 π r 2. Find the angle at the center of the sector. Area of a sector when the central angle is given in degrees.

The semicircle is likewise a sector of a circle which in this instance has two equal-sized sectors. The Whole circle πr 2. Each of these formulas is applied depending on the type of information given about the sector.

Replace θ with 63. The angle of the sector is 360 area of the sector ie. So the area of the sector with a central angle theta and having radius r will be.

Then the area of a sector of circle formula is calculated using the unitary method. θ AKB 180 - 117 63 degrees. α Sector Area.

If the angle of the sector is given in degrees then the formula for the area of a sector is given by Area of a sector θ. Area of a sector is a fractions of the area of a circle. If the central angle is then the area of sector of circle formula will be.

A θ 360 π r 2. A sector has 15th the area of a circle with a radius of 5 cm. Find the area of the sea where ships.

The basic formula for the area of a circle area pi r2 can be applied to find the area of sectors of the circle The full circle has an angle of 2 pi radians around the centre. The same method may be used to find arc length - all you need to remember is the formula for a circles circumference. Find the area of the sector of a circle with radius 3 cm and of angle 20.

π 314 Given values radius 100 cm. Both can be calculated using the angle at the centre and the diameter or radius. A 1 4 π r 2.

From the proportion we can easily find the final sector area formula. To find the area of sector we will divide total area of the circle by 4 as. Area of a Sector of Circle 12 r 2 θ where θ is the sector.

Given the radius of the circle r and the angle of the sector θ the formula for calculating the sectors area is.


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