Question

-50 Points- Find the area of the smaller sector. Leave your answer in terms of pi.

Answer 1

The formula to find the area of a sector is:

A = $\frac{degree}{360} \pi r^{2}$

In this case:

Degree = 40

Radius = 8

^^^Plug these numbers into the formula given above

A = $\frac{40}{360} \pi 8^{2}$

Solve

A = $\frac{1}{9}$π8²

A =  $\frac{1}{9}$π64

A = $\frac{64}{9}\pi$

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 2

Answer:

7.1π

Step-by-step explanation:

Calculate what part of the angle 360° ​​is the given center angle 40°.

$\dfrac{40}{360}=\dfrac{1}{9}$

The same part of the area of the circle is the given sector.

The formula of an area of a circle:

$A=\pi r^2$

r - radius

We have r = 8.

The area of a circle:

$A_O=\pi(8^2)=64\pi$

The area of the sector:

$A=\dfrac{1}{9}A_O\to A=\dfrac{1}{9}(64\pi)=\dfrac{64}{9}\pi\approx7.1\pi$