Question

Circle L is shown. Line segments K L and M L are radii. The length of K L is 9. Angle M L K is 120 degrees. Sector M L K with a 120 degree angle is shaded.

What is the area of the shaded sector of the circle?

9Pi units squared
27Pi units squared
81Pi units squared
162Pi units squared

Answer 1

.27 pi

Explanation:

Answer 2

The area of the shaded sector of the circle is 27
`\pi` units squared, if the line segments KL and ML are radii, the length of KL is 9 units and MLK is 120 degrees.

Explanation:

The given is,

K L and M L are radii

Length of K L is 9

Angle M L K is 120 degrees

In the given question diagram is missing, so we attach the diagram.

Step:1

The shaded area of sector in the circle is
`(1)/(3)` of circle area.

( Three times of 120° equal to 360°)

Formula for area of circle,

`A = \pi r^(2)`.........................................(1)

From the ratio and area of circle formula for shaded sector is,

`A_(Shaded sector) =( \pi r^(2) )/(3)`.........................(2)

Where, r - radius of circle

From the given,

r = 9 units

Equation (2) becomes,

`A_(Shaded sector) =( \pi( 9)^(2) )/(3)`

`=( \pi 81)/(3)`

= 27
`\pi`

`A_(Shaded sector) =27 \pi` Units squared

Result:

The area of the shaded sector of the circle is 27
`\pi` units squared, if the line segments KL and ML are radii, the length of KL is 9 units and MLK is 120 degrees.