Question

What is the area of a sector with a central angle of 8 π/11 radians and a radius of 7.2 ft? 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 to help any of my fellow people who suck at math :)

Answer 1

`59.19 ft^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=7.2\ ft`

`\pi =3.14`

substitute

`A=(3.14)(7.2)^(2)`

`A=162.78\ ft^2`

step 2

we know that

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

so

using proportion

Find out the area of a sector with a central angle of 8 π/11 radians

`(162.78)/(2\pi )(ft^2)/(rad) =(x)/((8\pi/11))(ft^2)/(rad) \\\\x=162.78(8/11)/2\\\\x=59.19\ ft^2`