Question

What is the area of a sector with a central angle of (2pi/3) radians and a diameter of 12 in?

Answer 1

Answer:

The area of the sector is $37.68\ in^{2}$

Step-by-step explanation:

step 1

Find the area of the circle

The area of the circle is equal to

$A=\pi r^{2}$

we have

$r=12/2=6\ in$ ----> the radius is half the diameter

substitute

$A=(3.14)(6)^{2}$

$A=113.04\ in^{2}$

step 2

Find the area of a sector with a central angle of (2pi/3)

Remember that

The area of $113.04\ in^{2}$ subtends a central angle of $2\pi \ radians$

so

by proportion

Let

x----> the area of the sector

$\frac{2\pi}{113.04}=\frac{(2\pi/3)}{x}\\ \\x=113.04*(2\pi/3)/(2\pi)\\ \\x=37.68\ in^{2}$