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

Answer:

Area of circle = 9π

Step-by-step explanation:

Area of sector = $\frac{1}{2} \pi$

Its central angle = $\frac{1}{9}\pi \text{ radians}$

$\text{Area of sector} = \dfrac{\text{Central angle}}{2\pi} \times\text{Area of circle}$

$\text{Area of circle} = \text{Area of sector}\times\dfrac{2\pi}{\text{Central angle}}$

$A = \dfrac{1}{2}\pi\times\dfrac{2\pi}{\frac{1}{9}\pi} = 9\pi$