Respuesta :
Answer
Area of the sector = 31.42 square inches
Explanation
The area of a sector that has a central angle, θ, in a circle of radius r, is given as
[tex]\begin{gathered} \text{Area of a sector = }\frac{\theta}{360\degree}\times(Area\text{ of a circle)} \\ \text{Area of a circle =}\pi\times r^2 \\ \text{Area of a sector = }\frac{θ}{360°}\times\pi\times r^2 \end{gathered}[/tex]For this question,
θ = central angle = 100°
π = pi = 3.142
r = radius = 6 inches
[tex]\begin{gathered} \text{Area of a sector = }\frac{θ}{360°}\times\pi\times r^2 \\ \text{Area of a sector = }\frac{100\degree}{360\degree}\times3.142\times6^2=31.42\text{ square inches} \end{gathered}[/tex]Hope this Helps!!!
