Answer:
The area of the shaded sector is [tex]51.2\pi \ units^{2}[/tex]
Step-by-step explanation:
I assume that the problem is
Find the area of the shaded sector of the circle with radius equal to 16 units
step 1
Find the value of x
we know that
[tex]8x+2x=360\°[/tex]-----> by complete circle
[tex]10x=360\°[/tex]
[tex]x=36\°[/tex]
The central angle of the shaded sector is 2x
[tex]2(36\°)=72\°[/tex]
step 2
Find the area of the circle
The area of the circle is equal to
[tex]A=\pi r^{2}[/tex]
we have
[tex]r=16\ units[/tex]
substitute
[tex]A=\pi (16)^{2}[/tex]
[tex]A=256\pi\ units^{2}[/tex]
step 3
Find the area of the shaded sector
we know that
A central angle of 360 degrees subtends an area of circle equal to [tex]256\pi\ units^{2}[/tex]
so
by proportion
Find the area of the shaded sector by a central angle of 72 degrees
[tex]\frac{256\pi}{360}=\frac{x}{72} \\ \\ x=256\pi *(72)/360\\ \\x=51.2\pi \ units^{2}[/tex]
