Question

A circle with area 9π has a sector with a central angle of 1/9 π radians . What is the area of the sector?

PLEASE ANSWER WORTH 50 POINTS!!

Answer 1

Answer:

A = pi/2

Step-by-step explanation:

Area of a sector is given by

A = 1/2 r^2 theta when theta is given in radians

We know the area of the circle (pi * r^2) so we multiply by pi/pi

A = 1/2  pi/pi r^2 theta

A = 1/(2* pi)  * pi r^2 theta  

   =  1/(2* pi)  * Ac theta   where Ac is the area of a circle

Substituting what we know  Ac = 9 pi and theta = 1/9 * pi

A    =  1/(2* pi)  * 9*pi  1/9 * pi

A = 1/(2* pi)  * pi^2

A = 1/2 * pi

A = pi/2

Answer 2

Answer:

Its $\frac{\pi }{2}$ .

Step-by-step explanation:

Because the work shown below will show you how:

$\frac{\theta}{2\pi } = \frac{A_s}{A_c}\\\frac{1}{9} /2\pi = \frac{A_s}{9\pi } \\\frac{1}{18} = \frac{A_s}{9\pi } \\\frac{1}{18} * 9\pi = A_s\\=\pi/2$