Suppose that circles R and S have a central angle measuring 80°. Additionally, the measure of the sector for circle R is 329π 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
Accepted Solution
A:
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