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

Answer:

$59.19 ft^2$

Step-by-step 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

$\frac{162.78}{2\pi }\frac{ft^2}{rad} =\frac{x}{(8\pi/11)}\frac{ft^2}{rad} \\\\x=162.78(8/11)/2\\\\x=59.19\ ft^2$