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# sector area of a circle?

How do I find the radius of a sector of a circle if:

the area of the sector is 9.817 and the degree measure of the arc is 22.5.

How do I find the Radius??

### 6 Answers

- Anonymous1 decade agoFavorite Answer
Area of sector = Angle/360 x (pi x radius^2)

(Area of sector x 360)/ (Angle x pi) = radius^2

Take the root of this.

So it would be:

rt [(9.817 x 360)/(22.5 x 3.14)]

You work it out. I don't have a calculator.

- vlee1225Lv 61 decade ago
the formula is

Area of sector = 1/2 x radius^2 x angle in radians

so

let a = radius

Area = 9.817

pi = 3.14159265358979

Angle = 22.5 deg = 22.5 x pi/180 = 0.39269908169872 rad

so 1/2 x a^2 x 0.39269908169872 = 9.817

a^2 = 9.817 x 2 / 0.39269908169872

= 49.99757044266072

a = 7.0708960141315

- 5 years ago
The circle has center (0,0) with a radius of 2. The sector is defined by the angle between the hypotenuse of a triangle whose vertices are at O(0,0), B(^/2,^/2) and C(^/2,0) which is a right triagle with /_BOC = 45 degrees. and the hypotenuse of a triangle whose vertices are O(0,0) A(1,^/3) and D(0,1) which is a right triangle whose /_AOD = 60 degrees. The angle of the sector is /_AOD - /_BOC = 60 - 45 = 15 degrees. The area of the circle is (pi)r**2= (pi)(2)**2 = 4(pi) sq units. The circle entails 360 degrees and the sector is 15 degrees. The area of the sector AOB is (15/360)*(pi)=(pi)/24 sq units.

- 1 decade ago
Area of circle = PI * radius^2

Area of sector = Area of circle * angle/360

Use your algebra skills to solve these two equations for radius. Then plug and chug.

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- Anonymous1 decade ago
Area circle= pi*r*r Sector area= circle area*22.5/360

r=sq root (Sector area *360/pi *arc degrees)

r= sq root( 9.817*360/pi*22.5) = 7.070896

- ironduke8159Lv 71 decade ago
The area of the entire circle is 360/22.5 *9.817 = pir^2.

So r = sqrt(360*9.817/(22.5 pi)) = 7.07 approximately.