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?

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