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

The area of the sector is
`(\pi)/(2)\ units^2`

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

`(9\pi)/(2\pi)=(x)/((1)/(9)\pi) \\\\x=9\pi((1)/(9)\pi})/2\pi\\\\x=(\pi)/(2)\ units^2`