Answer: [tex]A_c=345.4\ cm^2[/tex]
Step-by-step explanation:
You need to analize the information given in the exercise.
By definition, there are 360 degrees in a circle.
In this case, you know that the Central angle in degrees of the given sector of the circle is the following:
[tex]C=45\°[/tex]
And the area of that sector is this one:
[tex]A_s=13.75\pi\ cm^2[/tex]
Then, you need to calculate the number of sectors in that circle.
In order to do it, you have to divide 360 degrees by the central angle of that sector. So, you get:
[tex]N\° Sectors=\frac{360\°}{45\°}=8[/tex]
Knowing that there are 8 sectors in the circle, you need to multiply the area of the sector given in the exercise by 8, in order to calculate the area of the circle.
Therefore, this is (Using [tex]\pi =3.14[/tex]):
[tex]A_c=8A_s\\\\A_c=(8)(13.75*3.14)\ cm^2\\\\A_c=345.4\ cm^2[/tex]
