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

Answer:

$9\pi$

Step-by-step explanation:

The area of a sector is given by;

$A= \frac{1}{2} {r}^{2} \theta$

From the given information, the central angle is

$\theta = \frac{ \pi}{9}$

and

$A= \frac{\pi}{2}$

Let us substitute and solve for the radius, r.

$\frac{ \pi}{2} = \frac{1}{2} \times {r}^{2} \times \frac{ \pi}{9}$

$1 = \frac{ {r}^{2} }{9}$

${r}^{2} = 9$

$r = \sqrt{9} = 3 \: units$

The area of a circle is given by:

$= \pi \: {r}^{2}$

Substitute the radius to get:

$= \pi \times {3}^{2} \\ = 9\pi$