Question

A circle has a sector with area \dfrac{1}{2}\pi 2 1 ​ πstart fraction, 1, divided by, 2, end fraction, pi and central angle of \purple{\dfrac{1}{9}\pi} 9 1 ​ πstart color #9d38bd, start fraction, 1, divided by, 9, end fraction, pi, end color #9d38bd radians . What is the area of the circle?

Answer 1

Area of circle = 9π

Explanation:

Area of sector =
`(1)/(2) \pi`

Its central angle =
`(1)/(9)\pi \text{ radians}`

`\text{Area of sector} = \frac{\text{Central angle}}{2\pi} *\text{Area of circle}`

`\text{Area of circle} = \text{Area of sector}*\frac{2\pi}{\text{Central angle}}`

`A = (1)/(2)\pi*(2\pi)/((1)/(9)\pi) = 9\pi`