Respuesta :

[tex]\bf \textit{area of a sector of a circle}\\\\ A=\cfrac{\theta \pi r^2}{360}\quad \begin{cases} r=radius\\ \theta =angle~in\\ \qquad degrees\\ -------\\ r=8\\ \theta = 40 \end{cases}\implies A=\cfrac{40\pi \cdot 8^2}{360}[/tex]

Answer:

Option A is correct.

Step-by-step explanation:

Given radius of the circle, r = 8 cm

Central Angle of the shaded Sector,  [tex]\theta[/tex] = 40°

Area of Sector is given by the following formula,

[tex]Area\:of\:Sector=\frac{\theta}{360^{\circ}}\times\pi r^2[/tex]

Putting given values we get,

Area of Sector = [tex]\frac{40}{360}\times\pi(8)^2[/tex]

                        = [tex]\frac{1}{9}\times3.14\times64[/tex]

                        = [tex]22.3\:cm^2[/tex]

Therefore, Option A is correct.

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