Answer:
4.5pi square units
Explanation:
Area of the sector is expressed as
[tex]A\text{ =}\frac{\theta}{360}\times\pi r^2[/tex]r is the radius of the circle
theta is the central angle
Given
theta = pi = 180 degrees
radius = diameter/2
radius = 6/2 = 3
Substitute the given values into the expression above;
[tex]\begin{gathered} A\text{ = }\frac{180}{360}\times\pi(3)^2 \\ A\text{ = }\frac{1}{2}\times9\pi \\ A\text{ = }\frac{9\pi}{2} \\ A\text{ = 4.5}\pi units^2 \end{gathered}[/tex]hence the area of the sector is 4.5pi square units
