Question 1210141
Let the sphere have radius $r$.
The largest possible cross-sectional area of the sphere is a circle with radius $r$, so its area is $\pi r^2$.
Given that the radius of the sphere is $r = \frac{1}{2}$, the largest possible cross-sectional area is $\pi (\frac{1}{2})^2 = \frac{\pi}{4}$.

The area of the cross section is 64\% of the largest possible cross-sectional area.
Therefore, the area of the cross section is $0.64 \cdot \frac{\pi}{4}$.
$$ 0.64 \cdot \frac{\pi}{4} = \frac{64}{100} \cdot \frac{\pi}{4} = \frac{16}{25} \cdot \frac{\pi}{4} = \frac{4\pi}{25} $$

Thus, the area of the cross section is $\frac{4\pi}{25}$.

Final Answer: The final answer is $\boxed{\frac{4 \pi}{25}}$