The circle with a radius of 6cm and a sector with a central angle measuring 60 degrees is sketched above. Note that the shaded sector that is bounded by two radii is shaded in peach color.
The area of a circle is derived as
[tex]A=\pi\times r^2[/tex]
Therefore, the area of a sector (cut out of a complete 360 degree circle) is derived as a fraction of the area of a circle. The central angle of the sector will be used to determine the "fraction" of the area as shown below;
[tex]\begin{gathered} \text{Area of a sector=}\frac{\theta}{360}\times\pi\times r^2 \\ \text{Where, }\theta=the\text{ central angle of the sector} \\ r=\text{radius, }\pi=3.14 \end{gathered}[/tex]
Pi is usually given as 3.14, except the question gives you another specific and different value. The solution now is;
[tex]\begin{gathered} \text{Area of shaded sector=}\frac{60}{360}\times3.14\times6^2 \\ \text{Area of shaded sector=}\frac{60}{360}\times3.14\times36 \\ \text{Area}=\frac{60\times3.14\times36}{360} \\ \text{Area}=\frac{6782.4}{360} \\ \text{Area}=18.84cm^2 \end{gathered}[/tex]
