Respuesta :

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

gmany

Answer:

7.1π

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]

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