Question

Suppose that circles A and B have a central angle measuring 100°. Additionally, the measure of the sector for circle A is 10π m2 and for circle B is 40π m2.

If the radius of circle A is 6 m, what is the radius of circle B?

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 A
rB------> radius circle B
A------> area sector A
B------> area sector B
rB²=B*rA²/A-------> 6²*[40π]/[10π]-------> 144--------> rB=√144
rB=12 m

the answer is
radius of circle B is 12 m