Question

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

Answer 1

`(7128)/(14)`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
`=(1)/(2)r^2*angle \ of \ the \ sector.`

We took angle = π

Plugging values in formula, we get

Area of the sector is =
`(1)/(2)(18^2 * \pi)`

=
`(1)/(2)(324 * \pi)`

= 162π

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

Therefore, area of the shaded sector is 144π.

Answer 2

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