what is the approximate area of the shaded sector in the circle shown below HELP FAST!!
Accepted Solution
A:
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!