Step-by-step explanation:

Volume of the cube of side 4cm = s³ = 4³ = 64

Volume of the cube of side 1cm = 1

Number of cubes of side 1cm that can be taken out from a cube of 4cm are 64/1 = 64cubes

Surface area of cube of side 4cm = 6s² = 6(4)² = 6*64cm²

Surface area of cube with side as 1cm = 6cm²

Surface areas of 64 cubes = 64*6cm²

Ratio 6*16 : 64*6

= 16:64

= 1:4

The ratio of the surface Ares of original cubes and the cut outs = 1:4

A cube of side 4 cm is painted on all its sides. If it is sliced in 1 cubic cm cubes, then number of such cubes that will have exactly two of their faces painted is_____ .

TOTAL NO OF 1 cm CUBES = 5 x 5 x 5 = 125

OF THIS ON EACH OF THE EXTERNAL SLICE 3 x 3 = 9 CUBES WILL HAVE ONLY ONE SIDE PAINTED. OF THE REMAINING 4 WILL HAVE PAINT ON THREE SIDES AND 12 WILL HAVE PAINT ON TWO SIDES.

TOTAL NUMBER OF CUBES THAT WOULD HAVE PAINT ON ONLY ONE SIDE = 6 x 9 = 54