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# Find the area of a circular sector?

1. Find the area of a sector with central angle 1 radian in a circle of radius 10m.

2. The area of a sector of a circle with a central angle of 2 radians is 16m^2. Find the radius of the circle.

Please help!

### 3 Answers

- Simple manLv 58 years agoFavorite Answer
Area of sector = (1/2) r² θ ,where θ should always be in radians and r is the radius of a circle

1. Area of sector =(1/2) (10)² (1)

=>50 m² <--

2. Area of sector = (1/2) r² θ = 16

=>(1/2)(r²)(2) = 16

=>r² =16

=> r = √16

=> r = 4 m <--

- ChrisLv 78 years ago
1.

There are 2 pi radians in a full circle.

The area of a circle of radius 10m is A = pi r^2 = pi (10m)^2 = 100 pi m^2.

The area of a sector with central angle 1 radian is (100 pi m^2) * (1 / (2 pi)) = 50 m^2

Answer: 50 m^2

2.

16 m^2 = (pi r^2) * (2 / (2 pi)) = pi r^2 * (1 / pi) = r^2

r^2 = 16 m^2

r = 4m

Answer: The radius is 4 meters.

- NickLv 68 years ago
The ratio of the angle (in radians) to the total angle of a circle (2pi) must be equal to the ratio of the area of the section and the total area of the circle.

angle(radians)/(2*pi) = area of sector/pi*r^2

=> area of sector = (angle/2*pi)*pi*r^2 = (1/2)angle*r^2

1. (1/2)*1x10^2 = 50 m^2

2. 16 = (1/2)*2*r^2 = r^2

=> r = 4 m