[tex]\text{Area}=63.66in^2[/tex]
Explanation
the area of a circle is given by:
[tex]\begin{gathered} \text{Area}=\pi\cdot radius^2 \\ so,\text{ the area of a circular sector} \\ \text{Area}=\frac{r^2\cdot\emptyset}{2}(\emptyset\text{ in radians)} \end{gathered}[/tex]
Step 1
convert the angle from degrees into radias
remember
[tex]2\text{ }\pi\text{ rad}\rightarrow360\text{ degr}ees[/tex]
so
[tex]114\text{ degr}es(\frac{2\text{ }\pi}{360\text{ deg}})=1.98\text{ radians}[/tex]
Step 2
Replace,
[tex]\begin{gathered} \text{Area}=\frac{r^2\cdot\emptyset}{2}(\emptyset\text{ in radians)} \\ \text{Area}=\frac{8^2\cdot(1.98)}{2} \\ \text{Area}=63.66in^2 \end{gathered}[/tex]
I hope this helps you
