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The lenght of arc ab of a circle with center at o is equal to twice the lenght of the raduis r of the circle. find the area of sector aob in terms of r.

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  • Réponse publiée par: jasminsexy

    42.41 cm^2


    Step-by-step explanation:

    A SECTOR is an area inside a circle which is enclosed by an arc and two radii with a certain angle.


    Recall that in finding the AREA OF A SECTOR, we use the formula


    A = (1/2)(r^2)(Θ)


    where A is the area;


    r is the radius; and


    Θ is the angle in radians


    Note that the angle is in "radians", so we should convert the given angle into radians. RADIAN is the standard unit used in angular measurements, and is also the SI unit in measuring angles. CONVERTING DEGREES TO RADIANS, we use the conversion factor π radians is equal to 180 degrees.


    We first convert 60 degrees to radians


    Θrad = (60°)( π rad / 180°)


    Θrad = π/3 rad


    Substituting the values in the equation, we have


    A = (1/2)(9cm)^2(π/3)


    A = \frac{27}{2}π

    Therefore, the area of the sector is \frac{27}{2}π or approximately 42.41 cm^2


    For more related problems involving area of sectors, see links below.

  • Réponse publiée par: kateclaire

    answer:

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  • Réponse publiée par: elaineeee
    Area of Sector

    A sector is like a "pizza slice" of the circle. It consists of a region bounded by two radii and an arc lying between the radii.

    The area of a sector is a fraction of the area of the circle. This area is proportional to the central angle. In other words, the bigger the central angle, the larger is the area of the sector.


    Formula for Area of Sector (in degrees)

    We will now look at the formula for the area of a sector where the central angle is measured in degrees.

    Recall that the angle of a full circle is 360˚ and that the formula for the area of a circle is πr2.

    Comparing the area of sector and area of circle, we derive the formula for the area of sector when the central angle is given in degrees.

    where r is the radius of the circle

    This formula allows us to calculate any one of the values given the other two values.

  • Réponse publiée par: sicienth
    Measure of arc divided by 360 then multiply it to the area of the circle
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The lenght of arc ab of a circle with center at o is equal to twice the lenght of the raduis r of th...