The area of a sector of a circle can be calculated by using the formula:
[tex]A=\frac{\theta}{360}\cdot\pi\cdot r^2\text{ where }\theta\text{ is the angle in degrees and r is the radius}[/tex]
The total area of a circle can be calculated as:
[tex]A_{total}=\pi\cdot r^2\text{ where r is the radius}[/tex]
To find the area of the shaded region, you need to calculate the total area of the circle and then subtract the area of the non-shaded region, as follows:
[tex]\begin{gathered} A_{total}=\pi\cdot r^2\text{ The given value for r is 3} \\ A_{total}=\pi\cdot3^2\text{ } \\ A_{total}=\pi\cdot9 \\ A_{total}=3.14\cdot9 \\ A_{total}=28.3 \end{gathered}[/tex]
Now let's calculate the area of the non-shaded region:
[tex]\begin{gathered} A=\frac{\theta}{360}\cdot\pi\cdot r^2\text{ the given values for }\theta=112\text{ and r=3} \\ A=\frac{112}{360}\cdot\pi\cdot3^2\text{ } \\ A=0.31\cdot3.14\cdot9 \\ A=8.8 \end{gathered}[/tex]
The area of the shaded region will be:
[tex]\begin{gathered} A_{SR}=A_{total}-A \\ A_{SR}=28.3_{}-8.8 \\ A_{SR}=19.5 \end{gathered}[/tex]
