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

We know that
When circles have the same central angle measure, the ratio of measure of the sectors is the same as the ratio of the radii squared.
so
rA²/rB²=A/B
where
rA-------> radius circle Q
rB------> radius circle R
A------> area sector Q
B------> area sector R
rB²=B*rA²/A-------> 7²*[9π]/[4π]-------> 110.25--------> rB=√110.25
rB=10.5 cm

the answer is
radius of circle R is 10.5 cm