Question

The measure of central angle qrs is startfraction 8 pi over 9 endfraction radians. what is the area of the shaded sector?

Answer 1

The area of the shaded sector is 144π units squared.

What is a sector?

• A circular sector, also known as a circle sector or disk sector, is a piece of a disk bounded by two radii and an arc, with the smaller area known as the minor sector and the larger area known as the major sector.

To find the area of the shaded sector:

Given - The central angle of the sector is, θ $=\frac{8\pi }{9} rad$.

The radius of the circle is, $R=18 units$.

We know that the area of a sector of a circle of radius 'R' and central angle θ is given as:

$A=\frac{1}{2} R^{2}$θ

Insert, θ $=\frac{8\pi }{9} ,R=18$ and obtain:

$A=\frac{1}{2} *18^{2} *\frac{8\pi }{9} \\A=\frac{(324*4)}{9} \pi \\A=(36*4)\pi \\A=144\pi units^{2}$

Therefore, the area of the shaded sector is 144π units squared.

Know more about sectors here:

https://brainly.com/question/22972014

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The complete question is given below:

The measure of central angle QRS is StartFraction 8 pi Over 9 EndFraction radians. What is the area of the shaded sector? 36Pi units squared 72Pi units squared 144Pi units squared 324Pi units squared