Question

Both circle Q and circle R have a central angle measuring 110°. The area of circle Q's sector is 4π cm2, and the area of circle R's sector is 9π cm2. The radius of circle Q is 7 cm. Which is the radius of circle R

Answer 1

The answer is 10.5 :)

Answer 2

The area of circle Q's sector = 4π
`cm^2`

the area of circle R's sector = 9π
`cm^2`

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)

`(Radius-R)/(Radius-Q) = \sqrt{(area-R)/(area-Q) }`

Plug in all the values

`(x)/(7) = \sqrt{( 9\pi)/( 4\pi )`

`(x)/(7) = \sqrt{(9)/(4)}`

`x = (3)/(2) * 7 = 10.5`

Therefore , the radius of circle R = 10.5 cm