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

Answer:

$151.98\ cm^{2}$

Step-by-step 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

$\frac{379.94}{2\pi}=\frac{x}{4\pi/5}\\ \\x=379.94*( 4\pi/5)/(2\pi)\\ \\x=151.98\ cm^{2}$