In the diagram, the radius of the larger circle is 3 times the radius of the smaller circle. What fraction of the area of the larger circle is not shaded?
(A) $\frac{8}{9}$
(B) $\frac{2}{3}$
(D) $\frac{7}{9}$
(E) $\frac{1}{3}$
(C) $\frac{5}{6}$

![](https://cdn.mathpix.com/cropped/2024_04_20_6027bc27089ed4fc493cg-012.jpg?height=247&width=244&top_left_y=2267&top_left_x=1339)
The fraction of the area of the larger circle that is not shaded does not depend on the actual radius of either circle, and so we begin by letting the radius of the smaller circle be 1 and thus the radius of the larger circle is 3 .

In this case, the area of the smaller circle is $\pi(1)^{2}=\pi$.

The area of the larger circle is $\pi(3)^{2}=9 \pi$.

The area of the larger circle that is not shaded is $9 \pi-\pi=8 \pi$.

Therefore, the fraction of the area of the larger circle that is not shaded is $\frac{8 \pi}{9 \pi}=\frac{8}{9}$.

(Alternately, we could note that the fraction of the area of the larger circle that is shaded is $\frac{\pi}{9 \pi}=\frac{1}{9}$ and so the fraction of the area of the larger circle that is not shaded is $1-\frac{1}{9}=\frac{8}{9}$.)

ANswer: (A)