Question

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?

Answer 1

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 is

the area of the sector for circle S is 8π ft²