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

Its
`(\pi )/(2)` .

Explanation:

Because the work shown below will show you how:

`(\theta)/(2\pi ) = (A_s)/(A_c)\\(1)/(9) /2\pi = (A_s)/(9\pi ) \\(1)/(18) = (A_s)/(9\pi ) \\(1)/(18) * 9\pi = A_s\\=\pi/2`

Answer 2

A = pi/2

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