Question

What is the area of a sector with a central angle of 2π9 radians and a diameter of 20.6 mm?

Use 3.14 for π and round your answer to the nearest hundredth.

Answer 1

`37.01\ mm^(2)`

Explanation:

we know that

The area of a circle is equal to

`A=\pi r^(2)`

we have

`r=20.6/2=10.3\ mm` ----> the radius is half the diameter

substitute

`A=(3.14)(10.3^(2))=333.1226\ mm^(2)`

`2\pi` radians subtends the complete circle of area
`333.1226\ mm^(2)`

so

by proportion

Find the area of a sector with a central angle of
`2\pi/9` radians

`(333.1226)/(2\pi)=(x)/(2\pi/9)\\ \\x=336.1226*( 2\pi/9)/(2\pi)\\ \\x=37.01\ mm^(2)`