Question

a cube of side 4 cm is cut into i cmcubes. the ratio of the surface areas of the original cubes and cut-out cubes is

Answer 1

SA of original cube = 6(4^2) = 96 cm^2

I will assume it will be cut into cubes, each one i cm on a side.
So number of such cubes = 4^3 / i^3

surface area of each small cube = 6i^2
total surface area of all the little cubes
= (4^3)/(i^3)*(6i^2)
= 64(6)/i = 384/i

so ratio of SA of original : SA of all little ones
= 96 : 384/i
= 1 : 4/i
= i : 4

If you meant that there will be i cubes to be cut out,
the calculations will require cube roots and square roots
let me know