Respuesta :

equestriangirl131
The area of the shaded sector is one-fourth of the area of the whole circle so:
[tex]area = r^2 \pi \\ area = 6^2 \pi \\ area = 36 \pi[/tex]
area of shaded region[tex] = \frac{36 \pi }{4} \\ area = 9[/tex]
The area of the shaded region is 9pi units^2

Answer:

The correct option is B.

Step-by-step explanation:

The area of a circle is

[tex]A=\pi r^2[/tex]

where, r is the radius of the circle.

The radius of the given circle is 6 units.

The area of given circle is

[tex]A=\pi (6)^2[/tex]

[tex]A=\pi (36)[/tex]

[tex]A=36\pi[/tex]

The area of complete circle is 36π units².

From the given figure it is clear that 1/4th part of circle is shaded. The area of 1/4 th circle is

[tex]A_1=\frac{1}{4}A[/tex]

[tex]A_1=\frac{1}{4}(36\pi)[/tex]

[tex]A_1=9\pi[/tex]

The area of shaded sector is 9π units². Therefore, the correct option is B.

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