-50 Points-
Find the area of the smaller sector.
Leave your answer in terms of pi.
The formula to find the area of a sector is:
A = [tex]\frac{degree}{360} \pi r^{2}[/tex]
In this case:
Degree = 40
Radius = 8
^^^Plug these numbers into the formula given above
A = [tex]\frac{40}{360} \pi 8^{2}[/tex]
Solve
A = [tex]\frac{1}{9}[/tex]π8²
A = [tex]\frac{1}{9}[/tex]π64
A = [tex]\frac{64}{9}\pi[/tex]
A = 7.1111111π
When rounded:
7.1π is the area of the sector
Hope this helped!
~Just a girl in love with Shawn Mendes
Answer:
Step-by-step explanation:
Calculate what part of the angle 360° is the given center angle 40°.
[tex]\dfrac{40}{360}=\dfrac{1}{9}[/tex]
The same part of the area of the circle is the given sector.
The formula of an area of a circle:
[tex]A=\pi r^2[/tex]
r - radius
We have r = 8.
The area of a circle:
[tex]A_O=\pi(8^2)=64\pi[/tex]
The area of the sector:
[tex]A=\dfrac{1}{9}A_O\to A=\dfrac{1}{9}(64\pi)=\dfrac{64}{9}\pi\approx7.1\pi[/tex]