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

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

Sis less than or equal to 75 (bottom left)