The area of the shaded sector of the circle is 27[tex]\pi[/tex] units squared, if the line segments KL and ML are radii, the length of KL is 9 units and MLK is 120 degrees.
Step-by-step 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 [tex]\frac{1}{3}[/tex] of circle area.
( Three times of 120° equal to 360°)
Formula for area of circle,
[tex]A = \pi r^{2}[/tex].........................................(1)
From the ratio and area of circle formula for shaded sector is,
[tex]A_{Shaded sector} =\frac{ \pi r^{2} }{3}[/tex].........................(2)
Where, r - radius of circle
From the given,
r = 9 units
Equation (2) becomes,
[tex]A_{Shaded sector} =\frac{ \pi( 9)^{2} }{3}[/tex]
[tex]=\frac{ \pi 81}{3}[/tex]
= 27[tex]\pi[/tex]
[tex]A_{Shaded sector} =27 \pi[/tex] Units squared
Result:
The area of the shaded sector of the circle is 27[tex]\pi[/tex] units squared, if the line segments KL and ML are radii, the length of KL is 9 units and MLK is 120 degrees.
