Respuesta :
Answer:
36π
Step-by-step explanation:
The area of a circle is given as:
[tex]A = \pi r^2[/tex]
where r = radius of the circle
The area of a sector of a circle is given as:
[tex]A_s = \frac{\alpha }{2\pi} * \pi r^2[/tex]
where α = central angle in radians
Since [tex]\pi r^2[/tex] is the area of a circle, A, this implies that:
[tex]A_s = \frac{\alpha }{360} * A[/tex]
A circle has a sector with area 33 pi and a central angle of 11/6 pi radians.
Therefore, the area of the circle, A, is:
[tex]33 \pi = \frac{\frac{11 \pi}{6} }{2 \pi} * A\\\\33\pi = \frac{11}{12} * A\\\\=> A = \frac{33\pi * 12}{11}\\ \\A = \frac{396 \pi}{11} \\\\A = 36\pi[/tex]
The area of the circle is 36π.
Answer:
[tex] A_{circle}= \frac{2\pi *33 \pi}{\frac{11 \pi}{6}}= 36\pi[/tex]
Then we can conclude that the area for the circle would be [tex] 36\pi[/tex]
Step-by-step explanation:
For this case we know that a sector have an area of [tex]33\pi[/tex] with a central angle of [tex]x=\frac{11\pi}{6}[/tex]
We know that the total area of a cricle is [tex] A= \pi r^2[/tex] and we want to find the area of the circle and we can use the following proportional rule:
[tex] A_s = \frac{x}{2\pi} A_{circle}[/tex]
From the last equation we can solve for [tex]A_{circle}[/tex] and we got:
[tex] A_{circle}= \frac{2\pi A_s}{x}[/tex]
And replacing we got:
[tex] A_{circle}= \frac{2\pi *33 \pi}{\frac{11 \pi}{6}}= 36\pi[/tex]
Then we can conclude that the area for the circle would be [tex] 36\pi[/tex]
