Suppose that circles a and b have a central angle measuring 40°. additionally, circle a has a radius of 5 2 ft and the radius of circle b is 9 2 ft. if the measure of the sector for circle a is 25 36 π ft2, what is the measure of the sector for circle b?

Let 

rA> radius of the circle A

rB> radius of the circle B

SA> the area of the sector for circle A

SB> the area of the sector for circle B 

we have that

rA=5/2 ft

rB=9/2 ft

rA/rB=5/9> rB/rA=9/5

SA=(25/36)π ft²

we know that

if Both circle A and circle B have a central angle , the square of the ratio of the radius of circle A to the radius of circle B is equals to the ratio of the area of the sector for circle A to the area of the sector for circle B

(rA/rB) ^2=SA/SB> SB=SA*(rB/rA) ^2> SB=(9/5) ^2*(25/36)π--->

SB > (81/25)*(25/36) > 81/36 >  9/4π ft²

the answer is

the measure of the sector for circle B is (9/4)π ft²

45

step-by-step explanation:

30+15