we know that
The measure of the sector of circle R is 32π/9 m².
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 = 2πr²162π = 2πr²
Divide both sides by 2π:162π/2π = 2πr²/2π81 = r²
Take the square root of both sides:√81 = √r² r=9 m
the answer is the radius of circle S is r=9 m
alternative method
Let
rA--------> radius of the circle R
rB-------> radius of the circle S
SA------> the area of the sector for circle R
SB------> the area of the sector for circle S
we have that
rA=4 m
rB=?
SA=32π/9 m²
SB=18π m²
we know that
if Both circle A and circle B have a central angle , the square of the ratio of the radius of circle A to the radius of circle B is equals to the ratio of the area of the sector for circle A to the area of the sector for circle B
(rA/rB) ^2=SA/SB-----> rB²=(SB/SA)*rA²-----> rB²=(18π/32π/9)*4²-----> rB²=162/2
rB=9 m