Question

What is the area of a sector with a central angle of 10π/7 radians and a radius of 18.4 m? 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 for help :)

Answer 1

Answer:

$759.34\ m^2$

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

$r=18.4\ m$

substitute

$A=\pi(18.4)^{2}$

$A=338.56\pi\ m^{2}$

step 2

we know that

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

so

using proportion

Find out the area of a sector with a central angle of 10π/7 radians

$\frac{338.56\pi}{2\pi } =\frac{x}{(10\pi/7)}\\\\x=(10\pi/7)(338.56)/2\\\\x=241.829\pi\ m^2$

use

$\pi =3.14$

$241.829(3.14)=759.34\ m^2$