Area of circles and sectors?

The area of a sector is 5pie cm. The central angle of the sector is 100 degrees. What is the radius of the circle

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  • 10 years ago
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    The problem states: "The area of a sector is 5pie cm."

    I will assume it should state: "The area of a sector is 5pie cm^2."

    Make a ratio involving the areas and angles of the arc and the entire circle:

    (Angle of the arc / Angle of the entire circle) = (Area of arc / Area of entire circle )

    100 / 360 = 5 pi / ( pi r^2 )

    The pi's cancel. Multiply by 360r^2 on both sides.

    100 r^2 = 360(5)

    100 r^2 = 1800

    Divide by 100 on both sides

    r^2 = 18

    Square root both sides

    r = sqrt (18)

    Answer:

    r = 4.2 cm

  • 10 years ago

    area of a sector =(Θ/360)Пr^2

    given area =5П

    Θ =100

    5П=(100/360)Пr^2

    5П *360/100*П =r^2

    18=r^2

    r =√18

    r=4.24cm

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