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.

Please help!

3 Answers

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  • 8 years ago
    Favorite 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 <--

  • 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

    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.

  • 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.

    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

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