Question

hat is the area of a sector with a central angle of 4π5 radians and a radius of 11 cm? Use 3.14 for π and round your final answer to the nearest hundredth

Answer 1

4/5 PI radians = 144 degrees
sector area = central angle / 360 * PI * radius^2
sector area = 144 / 360 * PI * 11^2
sector area = 152.0530844337 square centimeters
sector area = 152.05 square centimeters

Answer 2

`151.98\ cm^(2)`

Explanation:

we know that

The area of a circle is equal to

`A=\pi r^(2)`

we have

`r=11\ cm`

substitute

`A=(3.14)(11^(2))=379.94\ cm^(2)`

`2\pi` radians subtends the complete circle of area
`379.94\ cm^(2)`

so

by proportion

Find the area of a sector with a central angle of
`4\pi/5` radians

`(379.94)/(2\pi)=(x)/(4\pi/5)\\ \\x=379.94*( 4\pi/5)/(2\pi)\\ \\x=151.98\ cm^(2)`