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

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

We are given radius of the given circle = 18 units.

The shown angle of the sector is a little smaller than π radians.

Let us take it π radians.

We know formula for area of a sector is

We took angle = π

Plugging values in formula, we get

Area of the sector is =

=

= 162π

The nearest value of 162π in the given options is 144π .

Therefore, area of the shaded sector is 144π.

Check Hathaway they will