# 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

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)

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