Answer:
74.02 square meters.
Step-by-step explanation:
We are asked to find the area of sector of circle, whose central angle is [tex]\frac{2\pi}{15}[/tex].
We will use area of sector formula to solve our given problem.
[tex]\text{Area of sector}=\frac{\theta}{2\pi}\times \pi r^2[/tex], where, r represents radius of circle.
Upon substituting our given values in above formula, we will get:
[tex]\text{Area of sector}=\frac{\frac{2\pi}{15}}{2\pi}\times \pi (18.8)^2[/tex]
Using fraction rule [tex]\frac{\frac{a}{b}}{c}=\frac{a}{bc}[/tex], we will get:
[tex]\text{Area of sector}=\frac{2\pi}{15\times 2\pi}\times \pi (18.8)^2[/tex]
[tex]\text{Area of sector}=\frac{1}{15}\times \pi \times 353.44[/tex]
[tex]\text{Area of sector}=23.5626666\times \pi[/tex]
[tex]\text{Area of sector}=74.0243004\approx 74.02[/tex]
Therefore, the area of given sector of circle is 74.02 square meters.
