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