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13 June, 04:28

Suppose that circles R and S have a central angle measuring 80°. Additionally, the measure of the sector for circle R is

32

9

π m2 and for circle S is 18π m2.

If the radius of circle R is 4 m, what is the radius of circle S?

A) 6 m

B) 9 m

C) 12 m

D) 15 m

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Answers (1)
  1. 13 June, 04:30
    0
    The correct answer is B) 9 m.

    The measure of the sector of circle R is 32π/9 m. The measure of the central angle is 80°. This means that the sector is 80/360 = 2/9 of the circle. The area of a circle is given by A=πr², so the area of the sector is A=2/9πr². To verify this, 2/9π (4²) = 2/9π (16) = 32π/9.

    Using this same formula for circle S, we will work backward to find the radius:

    18π = 2/9πr²

    Multiply both sides by 9:

    18*9π = 2πr²

    162π = 2πr²

    Divide both sides by 2π:

    162π/2π = 2πr²/2π

    81 = r²

    Take the square root of both sides:

    √81 = √r²

    9 = r
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