The area of a [tex]30^{\circ}[/tex] sector of this circle is [tex]8\pi \ m^2[/tex]. The correct option is B. [tex]8\pi \ m^2[/tex].
Given,
The area of circle is [tex]96 \pi \ m^2[/tex].
We have to calculate the area of [tex]30^{\circ}[/tex] sector of this circle.
Area of circle:
We know that, Area of circle is,
[tex]A=\pi r^{2}[/tex]
Here, [tex]96\pi =\pi r^{2}[/tex]
Or,
[tex]r^{2} =96[/tex]
[tex]r=\sqrt{96}[/tex]
[tex]r=4\sqrt{6}[/tex]
So, radius of the circle,
[tex]r=4\sqrt{6}[/tex] [tex]m[/tex].
Now we know that Area of a Sector of Circle
Say [tex]A_{1}[/tex],
[tex]A_{1} = \frac{\Theta}{360} \pi r^{2}[/tex]
where [tex]\Theta[/tex] is the angle subtended at the center, given in degrees, and '[tex]r[/tex]' is the radius of the circle.
So,
[tex]A_{1} =\frac{30}{360} \pi (4\sqrt{6} )^{2}[/tex]
[tex]A_{1} =\frac{1}{12} \pi \times96[/tex]
[tex]A_{1} =8\pi \ m^2[/tex].
Hence the area of a [tex]30^{\circ}[/tex] sector of this circle is [tex]8\pi \ m^2[/tex]. the correct option is B [tex]8\pi \ m^2[/tex].
For more details on Area of Sector of circle follow the link:
https://brainly.com/question/3432053
