Question

A circle with radius 3 has a sector with central angle 1/9 pi radians what is the area of the sector

Answer 1

Answer:

The area of the sector is  $\frac{\pi}{2}\ units^2$

Step-by-step explanation:

step 1

Find the area of complete circle

$A=\pi r^2$

we have

$r=3\ units$

substitute

$A=\pi 3^2\\A=9\pi\ units^2$

step 2

Find the area of the sector

we know that

The area of complete circle subtends a central angle of 2π radians

so

using proportion

Find out the area of a sector by a central angle of 1/9 pi radians

$\frac{9\pi}{2\pi}=\frac{x}{\frac{1}{9}\pi} \\\\x=9\pi(\frac{1}{9}\pi})/2\pi\\\\x=\frac{\pi}{2}\ units^2$