lana
Lv 5
lana asked in Science & MathematicsMathematics · 8 years ago

# 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.

Relevance
• 8 years ago

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 <--

• Chris
Lv 7
8 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

2.

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

r^2 = 16 m^2

r = 4m

• Nick
Lv 6
8 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.