Area of circle given arc length?

number 50?

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2 Answers

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  • 4 months ago

    Answer : Option C is correct.

    It can be clearly shown that --

    The two circles have the same radius (r) and PS = ST = PR = RT

    Also M is midpoint of RS so that MS = MR = r/2

    Hence cos θ = MS/PS = (r/2) / r  =  1/2

    => θ = 60° , therefore,  Angle PST =  120°

    Consider circle with center S :

    Arc PRT subtends 120° at the center. 

    Hence its length PRT ( given = 2 π )  =  (120/360) * 2 π r

    => r/3  =  1 

    =>  r  =  3 

    Hence area of the circle =  π (3)² =  9 π  ...................... Answer

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  • 4 months ago

    PRS and RST have sides that are all equal to the radius, so they are both equilateral triangles. 

    The angles of an equilateral triangle are all 60° so angle PRT is 120° and the arc PRT is equal to 1/3 of a full circle.

    The circumference of the full circle will be 6π which means the radius is 3.

    C = 2πr = 6π --> r = 3

    From that you can easily find the area:

    A = πr²

    A = 3² * π

    A = 9π

    Answer:

    (C) 9π

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