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)

$\frac{Radius-R}{Radius-Q} = \sqrt{\frac{area-R}{area-Q} }$

Plug in all the values

$\frac{x}{7} = \sqrt{\frac{ 9\pi}{ 4\pi }$

$\frac{x}{7} = \sqrt{\frac{9}{4}}$

$x = \frac{3}{2} * 7 = 10.5$

Therefore , the radius of circle R = 10.5 cm