Question

PLEEASSSSEEEE HHEEEEELLLLPPPPPPPP !!!!!!!!!!!!!!!!!!!!!!!!!!! Circle R is shown. Line segments Q R and S R are radii. The length of Q R is 18. Sector Q R S is shaded. 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

Answer 1

Answer:

144

Step-by-step explanation:

Answer 2

Answer:

$144\pi\ un^2.$

Step-by-step explanation:

In the attached diagram, circle R is shown. Line segments QR and SR are radii and QR = SR = 18 units.

The measure of the central angle QRS is $\dfrac{8\pi}{9}$

1. Find the area of the whole circle:

$A_{circle}=\pi r^2=\pi \cdot 18^2=324\pi \ un^2.$

2. Note that the whole circle is determined by the full rotation angle with measure $2\pi$ radians. So,

$\begin{array}{cc}\text{Angle}&\text{Area}\\ \\2\pi &324\pi \\ \\\dfrac{8\pi }{9}&A_{sector}\end{array}$

So, write a proportion:

$\dfrac{2\pi}{\frac{8\pi}{9}}=\dfrac{324\pi}{A_{sector}}$

Cross multiply

$2\pi \cdot A_{sector}=324\pi \cdot \dfrac{8\pi }{9}\\ \\A_{sector}=162\pi \cdot \dfrac{8}{9}=144\pi\ un^2.$