Question

A circle has a sector with area 33 pi and a central angle of 11/6 pi radians. What is the area of a circle?

Answer 1

Answer:

$A_{circle}= \frac{2\pi *33 \pi}{\frac{11 \pi}{6}}= 36\pi$

Then we can conclude that the area for the circle would be $36\pi$

Step-by-step explanation:

For this case we know that a sector have an area of $33\pi$ with a central angle of $x=\frac{11\pi}{6}$

We know that the total area of a cricle is $A= \pi r^2$ and we want to find the area of the circle and we can use the following proportional rule:

$A_s = \frac{x}{2\pi} A_{circle}$

From the last equation we can solve for $A_{circle}$ and we got:

$A_{circle}= \frac{2\pi A_s}{x}$

And replacing we got:

$A_{circle}= \frac{2\pi *33 \pi}{\frac{11 \pi}{6}}= 36\pi$

Then we can conclude that the area for the circle would be $36\pi$

Answer 2

Answer:

36π

Step-by-step explanation:

The area of a circle is given as:

$A = \pi r^2$

where r = radius of the circle

The area of a sector of a circle is given as:

$A_s = \frac{\alpha }{2\pi} * \pi r^2$

where α = central angle in radians

Since $\pi r^2$ is the area of a circle, A, this implies that:

$A_s = \frac{\alpha }{360} * A$

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:

$33 \pi = \frac{\frac{11 \pi}{6} }{2 \pi} * A\\\\33\pi = \frac{11}{12} * A\\\\=> A = \frac{33\pi * 12}{11}\\ \\A = \frac{396 \pi}{11} \\\\A = 36\pi$

The area of the circle is 36π.