The area of circle Q's sector = 4π [tex] cm^2 [/tex]
the area of circle R's sector = 9π [tex] cm^2 [/tex]
The radius of circle Q = 7 cm
We need to find the radius of circle R that is x
Given : Both circle Q and circle R have a central angle measuring 110°
So the radius of circle R to the radius of circle Q is equal to the square root (area of circle R to the radius of circle Q)
[tex] \frac{Radius-R}{Radius-Q} = \sqrt{\frac{area-R}{area-Q} } [/tex]
Plug in all the values
[tex] \frac{x}{7} = \sqrt{\frac{ 9\pi}{ 4\pi } [/tex]
[tex] \frac{x}{7} = \sqrt{\frac{9}{4}} [/tex]
[tex] x = \frac{3}{2} * 7 = 10.5 [/tex]
Therefore , the radius of circle R = 10.5 cm
