3. Given that the distance from the center of the sphere to the plane passing through points $A, B, C$ on the sphere is half the radius of the sphere, and $A B=B C=C A=2$, then the surface area of the sphere is ( ).
A. $\frac{16 \pi}{9}$
B. $\frac{8 \pi}{3}$
C. $4 \pi$
D. $\frac{64 \pi}{9}$
3. Choose D. Reason: Obviously, if we first find the radius $R$ of the sphere, and then find the surface area, it would be overcomplicating a simple problem. Since $S_{\text {球 }}=4 \pi R^{2}$, combining this with the options, we only need to estimate the radius $R$ of the sphere.

Because the radius $R$ of the sphere is no less than the radius $r=\frac{2 \sqrt{3}}{3}$ of the circumcircle of $\triangle A B C$, then $S_{\text {球 }}=4 \pi R^{2} \geqslant 4 \pi\left(\frac{2 \sqrt{3}}{3}\right)^{2}=\frac{16 \pi}{3}>5 \pi$, hence we should choose D.