Question

What is the area of a sector with a central angle of 10π/7 radians and a radius of 18.4 m? use 3.14 for π and round your final answer to the nearest hundredth. enter your answer as a decimal in the box.

this is just for help :)

Answer 1

`759.34\ m^2`

Explanation:

step 1

Find the area of the circle

The area of the circle is equal to

`A=\pi r^(2)`

we have

`r=18.4\ m`

substitute

`A=\pi(18.4)^(2)`

`A=338.56\pi\ m^(2)`

step 2

we know that

The area of complete circle subtends a central angle of 2π radians

so

using proportion

Find out the area of a sector with a central angle of 10π/7 radians

`(338.56\pi)/(2\pi ) =(x)/((10\pi/7))\\\\x=(10\pi/7)(338.56)/2\\\\x=241.829\pi\ m^2`

use

`\pi =3.14`

`241.829(3.14)=759.34\ m^2`