PYQ · TGPSC Group I 2023 · Preliminary Test · Q139 Difficulty 3/5
Direction, Clocks, Calendars & Space› Cubes, Dice & Spatial Visualisation
A large cube is painted on all six faces. Now it is cut into a certain number of smaller identical cubes. It was found that among the smaller cubes, there were eight cubes which don’t have any faces painted. How many small cubes have exactly two faces painted ?
Answer d.
Explanation Answer · d
Option d: there are four cubes along each edge, giving 12 × 2 = 24 cubes with exactly two painted faces. If there are n small cubes along each edge, the unpainted interior cubes number (n−2)^3. Thus (n−2)^3 = 8 gives n=4. Exactly two painted faces occur along the twelve edges excluding corners: 12(n−2) = 12×2 = 24.
Prepared with PrepKar AI and checked; it may contain errors.