Q:

The measure of central angle QRS is radians. What is the area of the shaded sector? 36 72 144 324

Accepted Solution

A:
the picture in the attached figure

we know that

the angle measurement of central angle QRS is less than pi radians


area of the circle=pi*r²
for r=18 units
area of the circle=pi*18²------> 324*pi units²
area of ​​the half of a circle=324*pi/2-----> 162*pi units²
area of ​​a quarter of a circle=324*pi/4----> 81*pi units²

analyzing the graph we can say that the shaded area is smaller than the area of ​​the middle of a circle but it is larger than the area of ​​a quarter of a circle
so
the area of the shaded sector < 162*pi units²
and
the area of the shaded sector > 81*pi units²

therefore
the answer must be 144*pi units²