Question

2) 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?

Answer 1

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