Answer:
[tex]A=324\pi \text{ units}^2\approx1017.88\text{ units}^2[/tex]
Step-by-step explanation:
The formula for arc length is:
[tex]\stackrel{\frown}{A}=2\pi r(\frac{\theta}{360}})[/tex]
Where Θ is measured in degrees.
We know that the arc length is 8π when the degree is 80. So, substitute 8π for A and 80 for Θ:
[tex]8\pi=2\pi r(\frac{80}{360})[/tex]
Divide both sides by 2π:
[tex]4=r\frac{80}{360}[/tex]
Simplify the fraction:
[tex]4=\frac{2}{9}r[/tex]
Multiply both sides by 9/2:
[tex]r=18[/tex]
So, the radius is 18.
Now, we can find the area of the circle. The formula for the area of a circle is:
[tex]A=\pi r^2[/tex]
Substitute 18 into r:
[tex]A=\pi (18)^2[/tex]
Simplify:
[tex]A=324\pi \text{ units}^2\approx1017.88\text{ units}^2[/tex]
And we're done!
