The scale factor between two similar figures is 4 : 9. The ratio of the surface area of the larger figure to that of the smaller figure is given by (9/4)^2 = 81/16. It has to be noted that this is true here as the two figures are similar. Similarly the ratio of the volume of the larger figure to that of the smaller figure is (9/4)^3 = 729/64.

As the surface area of the smaller figure is 256, the surface area of the larger figure is 256*(81/16) = 1296 km^2. And the volume of the larger figure is 1536*(729/64) = 17496 km^3.

**The required surface area and volume of the larger figure is 1296 km^2 and 17496 km^3 resp.**