Cubes

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  1. If total number of cuts is 10 then find the minimum number of pieces that can be obtained.








  1. View Hint View Answer Discuss in Forum

    If total number of cuts is 10 then minimum number of pieces is 11 when cut is made in one plane only.

    Correct Option: B

    If total number of cuts is 10 then minimum number of pieces is 11 when cut is made in one plane only.

Direction: 216 cubes of similar size are arranged in the form of the bigger cube (6 cubes on each side, i.e.., 6 x 6 x 6) all the exposed surfaces are painted.

  1. How many of the cubes have at least 2 faces painted?








  1. View Hint View Answer Discuss in Forum

    Since total number of cubes is hence in the formula we will substitute n = 6
    At least 2 faces painted means number of cubes with 2 face painted + number of cubes with 3 face painted = 96 + 8 = 104.

    Correct Option: B

    Since total number of cubes is hence in the formula we will substitute n = 6
    At least 2 faces painted means number of cubes with 2 face painted + number of cubes with 3 face painted = 96 + 8 = 104.

  1. How many of the cubes have at most faces painted?








  1. View Hint View Answer Discuss in Forum

    Since total number of cubes is hence in the formula we will substitute n = 6
    At most 2 faces painted means number of cubes with 0 face painted + number of cubes with 1 face painted + number of cubes
    with 2 face painted = 64 + 48 + 96 = 208

    Correct Option: A

    Since total number of cubes is hence in the formula we will substitute n = 6
    At most 2 faces painted means number of cubes with 0 face painted + number of cubes with 1 face painted + number of cubes with 2 face painted = 64 + 48 + 96 = 208

  1. How many of the cubes have 2 most faces painted?








  1. View Hint View Answer Discuss in Forum

    Since total number of cubes is hence in the formula we will substitute n = 6
    Number of the cubes with 2 faces painted is 6(6 - 2)2
    = 6 x 16 = 96

    Correct Option: C

    Since total number of cubes is hence in the formula we will substitute n = 6
    Number of the cubes with 2 faces painted is 6(6 - 2)2
    = 6 x 16 = 96

  1. How many of the cubes have 0 faces painted?








  1. View Hint View Answer Discuss in Forum

    Since total number of cubes is hence in the formula we will substitute n = 6
    Number of the cubes with 0 faces painted is (6 - 2)3 = 43 = 64

    Correct Option: A

    Since total number of cubes is hence in the formula we will substitute n = 6
    Number of the cubes with 0 faces painted is (6 - 2)3 = 43 = 64