1056
1024
864
729

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First, we find the total surface area of each of the 3x3x3 cubes after they have been “diminished”. We will find it separately as the surface area on the outside and the surface area on the inside. If you visualize this figure, it has eight 1x1x1 cubes on each face, so the surface area of each face is 8. So the total surface area

on the outsideis 8 x (1x1) per face x 6 faces = 48Each “hole” at the surface has four faces. The surface area on the inside is 4 x (1x1) = 4 There are six such holes. So total surface area

on the insideis 4x6 = 24Now 20 of these “diminished” 3x3x3 pieces are fitted together to form our final figure. When two pieces are fitted together, some surface area is lost from

the outside portionfor both pieces. But the area from the inside portion is not lost like this.We have 8 corner pieces and 12 edge pieces. Corner pieces will lose (3/6) of their outside area because they are connected to other pieces on 3 out of 6 sides, while edge pieces will lose (2/6) of their outside area because they are connected to other pieces on 2 out of 6 sides.

Thus, for corner pieces, area = 48 x (1 - 3/6) + 24 = 48 For edge pieces, area = 48 x (1 - 2/6) + 24 = 56

Total surface area = 48x8 + 56x12 = 1056.