MATH SOLVE

2 months ago

Q:
# 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?

Accepted Solution

A:

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