Suppose that circles R and S have a central angle measuring 80°. Additionally, circle R has a radius of 3 ft and the radius of circle S is 6 ft. If the measure of the sector for circle R is 2π ft2, what is the area of the sector for circle S?

Let  rA--------> radius of the circle R rB-------> radius of the circle S SA------> the area of the sector for circle R SB------> the area of the sector for circle S   we have that rA=3 ft rB=6 ft rA/rB=3/6----> 1/2-----------> rB/rA=2 SA=2π 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=(2) ^2*(2π)---> SB----------- > 8π ft²
the answer isthe area of the sector for circle S is 8π ft²