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What is the area of the shaded region in the given circle in terms of pi and in simplest form.



A. (270pi +54radical3) m^2
B. (216 pi +54radical3) m^2
C. (216 pi + 81radical3) m^2
D. (270 pi +81radical3) m^2

Respuesta :

AnikaK
The correct answer is D. (270pi + 81radical3) m^2
dacotacrosby

Answer:

 

D. (270 pi +81radical3) m^2

Step-by-step explanation:

In order to determine the area of the shaded region, we need to  

determine the area of the circle, the sector and the triangle  

that is a part of the sector. Do the following steps and work:

Area of the circle:

πr² = π(18)² = 324π

Area of the sector:

(60/360) (324Ï€) = 54Ï€

Area of the triangle:

60/2=30

1/2 (b)(h) = 1/2 (18cos30)(18) = 81√3

Area of the shaded region:

324π - 54π + 81√3 = 270π + 18√3

The answer is D. (270π + 18√3)m²

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