Question

Find the area the sector.arc circle 10A. 16π mi²B. 34π/3 mi²C. 5π/3 mi²D. 9π mi²

Answer 1

Answer:$\frac{14\pi}{3}mi^2$Explanation:

The area of a sector is given as:

$\begin{gathered} Area\text{ = }\frac{\theta}{360}\times\pi r^2 \\ \\ \end{gathered}$

The sector angle, θ = 360° - 255°

θ = 105°

The radius, r = 4 mi

Substitute these values into the equation to solve for the area

$\begin{gathered} Area=\frac{105}{360}\times\pi\times4^2 \\ \\ Area=\frac{105}{360}\times16\pi \\ \\ Area=\frac{7}{24}\times16\pi \\ \\ Area=\frac{7}{3}\times2\pi \\ \\ Area=\frac{14\pi}{3}mi^2 \\ \end{gathered}$