Answer :
Complete question:
A circle with radius 3 has a sector with a central angle of 1/9 pi radians
what is the area of the sector?
Answer:
The area of the sector = [tex] \frac{\pi}{2}[/tex] square units
Step-by-step explanation:
To find the area of the sector of a circle, let's use the formula:
[tex] A = \frac{1}{2} r^2 \theta [/tex]
Where, A = area
r = radius = 3
[tex] \theta = \frac{1}{9}\pi [/tex]
Substituting values in the formula, we have:
[tex] A = \frac{1}{2}*3^2* \frac{1}{9}\pi [/tex]
[tex] A = \frac{1}{2}*9* \frac{1}{9}\pi [/tex]
[tex] A = 4.5 * \frac{1}{9}\pi [/tex]
[tex] A = \frac{\pi}{2}[/tex]
The area of the sector = [tex] \frac{\pi}{2}[/tex] square units