The formula to find the area of a circular sector if the angle is given in degrees is
[tex]\text{ Area of sector }=\frac{\theta}{360\text{\degree}}\cdot\pi r^2[/tex]
Where
So, for the area of the white circular sector you have:
[tex]\begin{gathered} \theta=32\text{\degree} \\ r=27.1\operatorname{mm} \\ \text{ Area of sector white }=\frac{32\text{\degree}}{360\text{\degree}}\cdot\pi(27.1mm)^2 \\ \text{ Area of sector white }=\frac{4}{45}\cdot\pi\cdot(27.1)^2mm^2 \\ \text{ Area of sector white }=\frac{4}{45}\cdot\pi\cdot734.41mm^2 \\ \text{ Area of sector white }=205.09mm^2 \end{gathered}[/tex]
And for the area of the gray circular sector you have:
[tex]\begin{gathered} \theta=360\text{\degree}-32\text{\degree}=328\text{\degree} \\ r=27.1\operatorname{mm} \\ \text{ Area of sector gray }=\frac{328\text{\degree}}{360\text{\degree}}\cdot\pi(27.1mm)^2 \\ \text{ Area of sector gray }=\frac{41}{45}\cdot\pi\cdot(27.1)^2mm^2 \\ \text{ Area of sector gray }=\frac{41}{45}\cdot\pi\cdot734.41mm^2 \\ \text{ Area of sector gray }=2102.13mm^2 \end{gathered}[/tex]
