Question

A circle with area 9pi has a sector with a central angle of 1/9 radians. What is the area of the sector?

Answer 1

`A=(1)/(2)`

Explanation:

The area of sector of a circle (in radians) is:

`A=(1)/(2)r^2 \theta`

Where

r is the radius

`\theta` is the angle of the sector

We know the angle but we need the radius.

We are given the total circle's area is
`9\pi`, putting in area of circle formula, we find the radius:

`\pi r^2=9\pi\\r^2=9\\r=3`

Now, using the values, we find the area of the sector:

`A=(1)/(2)r^2 \theta\\A=(1)/(2)(3)^2 ((1)/(9))\\A=(1)/(2)*9*((1)/(9))\\A=(1)/(2)`

Area of sector is
`(1)/(2)`