Question

A sector has an area of 1/2 π and the central angles of 1/9 π radians. What is the area of the circle?

Answer 1

Area of circle is 9π

Explanation:

The area of sector of a circle is given by
`A=(1)/(2)r^2\theta`

Plugging the given values in the formula, we get

`(1)/(2)\pi=(1)/(2)r^2\cdot(1)/(9)\pi`

Cancel out 1/2 and π from both sides, we are left with

`1=r^2\cdot(1)/(9)`

Cross multiplying, we get

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

Therefore, area of circle is given by

`A=\pi r^2\\\\A=\pi(3)^2\\\\A=9\pi`

Area of circle is 9π