Find the area of a sector of a circle of radius 1 foot swept by the angle 2pi/7.?

I do not understand how to do this. Please help!!!!!

Thank you!!

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  • 9 years ago
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    The area of a sector of circle of radius R swept by a central angle Θ (in radians---not degrees!) is

    A = ½ R²Θ.

    This is the ratio of the circle 2π/Θ of the area of the whole circle whose area is πR². Notice that the ratio gives the above formula

    A = πR²/(2π/Θ) = ½ R²Θ.

    Now use the formula. If Θ = 2π/7 and R = 1 ft

    A = ½ (1 ft)² (2π/7) = π/7 sq. ft.

  • 9 years ago

    The area of the complete circle with radius 1 is pi(r)^2 = pi(1)^2 = pi

    To sweep around the entire circle you'd go 360 degrees, which is 2pi in radians.

    You only want to sweep 2pi/7 radians. If the entire circle is 2pi radians, then 2pi/7 radians

    is 1/7 of the circle and wil account for 1/7 of the area of the whole circle.

    That makes the area of the section pi/7

  • 9 years ago

    Solution:

    angle = 2pi /7

    Radius r = 1 foot

    Formula for Area of sector = 1/2 * (angle) * radius^2

    = 1/2 * (2pi/7)* 1

    = 1/2 * (51.43)*1

    = 25.715 ft

  • 9 years ago

    area=pir^2

    area(total)=3.14(1^2)

    total area=3.14=pi

    area of a sector=(total area)(angle/2pi)

    area=(pi)(2pi/7/pi)

    area=pi(2/7)

    I assume the angle is in radians, if its degrees(which I doubt) use 360 instead of 2pi

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  • 9 years ago

    A= 3.14 squarefoot * 1/7)=0.45 squarefoot

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