Answer:
The area of the sector is [tex]\frac{\pi}{2}\ units^2[/tex]
Step-by-step explanation:
step 1
Find the area of complete circle
[tex]A=\pi r^2[/tex]
we have
[tex]r=3\ units[/tex]
substitute
[tex]A=\pi 3^2\\A=9\pi\ units^2[/tex]
step 2
Find the area of the sector
we know that
The area of complete circle subtends a central angle of 2π radians
so
using proportion
Find out the area of a sector by a central angle of 1/9 pi radians
[tex]\frac{9\pi}{2\pi}=\frac{x}{\frac{1}{9}\pi} \\\\x=9\pi(\frac{1}{9}\pi})/2\pi\\\\x=\frac{\pi}{2}\ units^2[/tex]
