MATH SOLVE

4 months ago

Q:
# 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?

Accepted Solution

A:

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

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