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Q69 (CISF/2025) Miscellaneous & General Knowledge › Important Days, Places & Events

A log of wood of dimension 7 ft x 3 ft × 1 ft is painted all over its surfaces. Then the log is cut into 21 cubes of equal sizes. The ratio of the number of cubes that are painted on 4 surfaces to that of cubes painted on 3 surfaces is :

Explanation

The log has dimensions 7 ft × 3 ft × 1 ft, resulting in 21 cubes of 1 ft3 each. Since the height of the log is only 1 ft, every cube is exposed on both the top and bottom faces, meaning every cube starts with 2 painted surfaces.

  • Cubes with 4 surfaces painted: These are the 4 corner cubes of the 7×3 arrangement. Each corner cube has 2 side faces exposed in addition to the top and bottom faces (2 + 2 = 4).
  • Cubes with 3 surfaces painted: These are the edge cubes that are not corners.
    • Along the 7 ft sides: There are (7 - 2) = 5 such cubes on each side. Total = 5 × 2 = 10.
    • Along the 3 ft sides: There is (3 - 2) = 1 such cube on each side. Total = 1 × 2 = 2.
    • Total cubes with 3 surfaces = 10 + 2 = 12.

The ratio of cubes with 4 surfaces painted to those with 3 surfaces painted is 4:12, which simplifies to 1:3.

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