The Solution:
Given:
[tex]\begin{gathered} central\text{ angle of a sector}=\theta=30^o \\ \\ diameter=6cm \\ \\ r=radius=\frac{6}{2}=3cm \end{gathered}[/tex]Required:
Find the area of a sector.
The formula for area:
[tex]Area=\frac{\theta}{360}\times\pi r^2[/tex]Substitute:
[tex]Area=\frac{30}{360}\times\pi(3)^2=\frac{\pi}{2}cm^2[/tex]Answer:
[tex]\frac{\pi}{2}cm^2\text{ or }0.5\pi cm^2[/tex]