Question

A circle has a sector with area 1/2π and central angle of 1/9π radians . What is the area of the circle? Either enter an exact answer in terms of π or use 3.14 and enter your answer as a decimal.

Answer 1

`9\pi`

Explanation:

The area of a sector is given by;

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

From the given information, the central angle is

`\theta = ( \pi)/(9)`

and

`A= (\pi)/(2)`

Let us substitute and solve for the radius, r.

`( \pi)/(2) = (1)/(2) * {r}^(2) * ( \pi)/(9)`

`1 = \frac{ {r}^(2) }{9}`

`{r}^(2) = 9`

`r = √(9) = 3 \: units`

The area of a circle is given by:

`= \pi \: {r}^(2)`

Substitute the radius to get:

`= \pi * {3}^(2) \\ = 9\pi`