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 :)
Accepted Solution
A:
Answer:[tex]59.19 ft^2[/tex]Step-by-step explanation:step 1Find the area of the circleThe area of the circle is equal to[tex]A=\pi r^{2}[/tex]we have[tex]r=7.2\ ft[/tex][tex]\pi =3.14[/tex]substitute[tex]A=(3.14)(7.2)^{2}[/tex][tex]A=162.78\ ft^2[/tex]step 2we know thatThe area of a circle subtends a central angle of 2π radianssousing proportionFind out the area of a sector with a central angle of 8 π/11 radians[tex]\frac{162.78}{2\pi }\frac{ft^2}{rad} =\frac{x}{(8\pi/11)}\frac{ft^2}{rad} \\\\x=162.78(8/11)/2\\\\x=59.19\ ft^2[/tex]