Can someone help me? I’ll reward 10 points + brainalist

Answer I got:
I got approximately 0.34906585039 in².
Step-by-step explanation:
So we know that [tex]A=\pi r^{2}[/tex]. We also know that [tex]r=\frac{1}{3}(0.3333...)[/tex] in. So, we can place this into our equation:
[tex]A=\pi\times\frac{1}{3}^{2}(A=\pi\times0.33333...^{2})[/tex]
Finally, we know that [tex]\pi\approx\frac{22}{7}[/tex].
[tex]A\approx\frac{22}{7}\times\frac{1}{3}^{2} (A=3.1415926...\times 0.3333333...^{2})[/tex]
This gave my final approx. answer of 0.34906585039 in².
[tex]\pi\frac{1}{3}^{2}\approx 0.34906585039[/tex]
All you need to do now is find the corresponding fraction to that!