Question

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

Answer 1

Answer:

$A=\frac{1}{2}$

Step-by-step explanation:

The area of sector of a circle (in radians) is:

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

Where

r is the radius

$\theta$  is the angle of the sector

We know the angle but we need the radius.

We are given the total circle's area is $9\pi$, putting in area of circle formula, we find the radius:

$\pi r^2=9\pi\\r^2=9\\r=3$

Now, using the values, we find the area of the sector:

$A=\frac{1}{2}r^2 \theta\\A=\frac{1}{2}(3)^2 (\frac{1}{9})\\A=\frac{1}{2}*9*(\frac{1}{9})\\A=\frac{1}{2}$

Area of sector is $\frac{1}{2}$