MATH SOLVE

4 months ago

Q:
# 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?

Accepted Solution

A:

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

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