Question

In circle Q with mZPQR = 86 and PQ = 18 units find area of sector PQR.
Round to the nearest hundredth.​

Answer 1

Answer:

The area of sector PQR is $243.04\ units^2$

Step-by-step explanation:

step 1

Find the area of complete circle Q

The area is given by the formula

$A=\pi r^{2}$

we have

$r=PQ=18\ units$

substitute

$A=\pi (18)^{2}$

$A=324\pi\ units^2$

step 2

Find the area of sector PQR

we know that

The area of complete circle subtends a central angle of 360 degrees

so

using a proportion

Find out the area that correspond to a central angle of 86 degrees

$\frac{324\pi}{360^o} =\frac{x}{86^o}\\\\x=324\pi (86)/360\\\\x=77.4\pi\ units^2$

assume

$\pi =3.14$

$77.4(3.14)=243.04\ units^2$