Respuesta :

Step 1. Find the total area of the circle using the formula:

[tex]A=\pi r^2[/tex]

Where r is the radius of the circle, in this case:

[tex]r=9in[/tex]

and π is a constant:

[tex]\pi=3.1416[/tex]

Substituting r and π into the formula for the area:

[tex]A=(3.1416)(9in)^2[/tex]

And solving the operations:

[tex]\begin{gathered} A=(3.1416)(81in^2) \\ A=254.47in^2 \end{gathered}[/tex]

Step 2. Find the are of the sector.

The sector is the part of the circle with an angle of 300°. We know that the total circle has 360°, thus, to find the area of the sector we have to divide the total area of the circle by 360, and then multiply by 300:

[tex]\frac{254.47in^2}{360}\times300[/tex]

Solving the operations:

[tex]=0.707in^2\times300[/tex][tex]=212.1in^2[/tex]

Answer: the area of the sector is

[tex]212.1in^2[/tex]