Answer: [tex]141 cm^{2}[/tex]
Step-by-step explanation:
We have two circles:
Cirlce 1, with a radius [tex]r=6 cm[/tex] and area [tex]A_{1}[/tex]:
[tex]A_{1}=\pi r^{2}[/tex]
And Cicle 2, with a radius [tex]R=9 cm[/tex] and area [tex]A_{2}[/tex]:
[tex]A_{1}=\pi R^{2}[/tex]
Since Circle 1 is inside Circle 2 and assuming the area of the shaded region is the shown in the attached image, its area is:
[tex]A=A_{2}-A_{1}=\pi R^{2}-\pi r^{2}[/tex]
[tex]A=\pi (R^{2}- r^{2})[/tex]
[tex]A=\pi ((9cm)^{2}- (6cm)^{2})[/tex]
Finally:
[tex]A=141.37 cm^{2} \approx 141 cm^{2}[/tex]
