Hello!
The answer is:
D. [tex]37.7cm^{2}[/tex]
Why?
To solve this problem, we need to remember the formula that defines the area of a circle.
The area of any circle is given by the following formula:
[tex]A=\pi *r^{2}[/tex]
We must remember that the expression "2π" radians is equal to 360° since π radian is equal to 180°.
Then,
[tex]\frac{360(degrees)}{30(degrees)}=12[/tex]
So,
[tex]\frac{360(degrees)}{12}=30(degrees)[/tex]
So, to calculate the area of the shaded area which represents 30° of the 360°, we need to divide the total area by 12.
[tex]A=\pi*r^{2}=\pi*(12cm)^{2}=\pi *144=144\pi =452.39cm^{2}[/tex]
Dividing by 12, we have:
[tex]A_{30(degrees)=\frac{452.39cm^{2}}{12}=37.7cm^{2}[/tex]
Hence, the correct option is:
D. [tex]37.7cm^{2}[/tex]
Have a nice day!
