Question

What is the area of the shaded sector?

A) 6 pi units2
B) 9 pi units 2
C) 18 pi units 2
D) 36pi units 2

Answer 1

The area of the shaded sector is one-fourth of the area of the whole circle so:

`area = r^2 \pi \\ area = 6^2 \pi \\ area = 36 \pi`
area of shaded region
`= (36 \pi )/(4) \\ area = 9`
The area of the shaded region is 9pi units^2

Answer 2

The correct option is B.

Explanation:

The area of a circle is

`A=\pi r^2`

where, r is the radius of the circle.

The radius of the given circle is 6 units.

The area of given circle is

`A=\pi (6)^2`

`A=\pi (36)`

`A=36\pi`

The area of complete circle is 36π units².

From the given figure it is clear that 1/4th part of circle is shaded. The area of 1/4 th circle is

`A_1=(1)/(4)A`

`A_1=(1)/(4)(36\pi)`

`A_1=9\pi`

The area of shaded sector is 9π units². Therefore, the correct option is B.