Question

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

Answer 1

Answer:
`(14\pi)/(3)mi^2`Step-by-step explanation:

The area of a sector is given as:

`\begin{gathered} Area\text{ = }(\theta)/(360)*\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=(105)/(360)*\pi*4^2 \\ \\ Area=(105)/(360)*16\pi \\ \\ Area=(7)/(24)*16\pi \\ \\ Area=(7)/(3)*2\pi \\ \\ Area=(14\pi)/(3)mi^2 \\ \end{gathered}`