Explanation:

- The surface area of a sphere is given by the formula $4\pi r^2$.

- When the surface areas of two spheres are in the ratio 64:81, the ratio of their radii is the square root of this, which is $\sqrt{\frac{64}{81}}=\frac{8}{9}$.

- The volume of a sphere is given by the formula $\frac{4}{3}\pi r^3$.

- Therefore, the ratio of their volumes is the cube of the ratio of their radii, i.e., $(\frac{8}{9}{)}^3=\frac{512}{729}$.

- Option 1: 512 : 729 is the correct answer.