Cubes

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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).Its all the 6 faces are painted with Green, Red, blue, black, white, orange colours.

  1. How many cubes are painted with red, blue, green and black?








  1. View Hint View Answer Discuss in Forum

    Here on each face 6 x 6 = 36 cubes that are painted with one colour.
    None of the cubes can be painted in four faces.

    Correct Option: D

    Here on each face 6 x 6 = 36 cubes that are painted with one colour.
    None of the cubes can be painted in four faces.

  1. Which of the following statement is correct
    (i) At least 1 cube is painted with red, green and blue.
    (ii) At most 1 cube is painted with red, green and blue.
    (iii) At most 6 cubes are painted with red and green.
    (iv) At least 6 cubes are painted with red and green.








  1. View Hint View Answer Discuss in Forum

    Here on each face 6 x 6 = 36 cubes that are painted with one colour.
    From solution of previous questions statements (ii) and (iii) are correct.

    Correct Option: B

    Here on each face 6 x 6 = 36 cubes that are painted with one colour.
    From solution of previous questions statements (ii) and (iii) are correct.

  1. How many cubes are painted with red or blue but not green?








  1. View Hint View Answer Discuss in Forum

    Here on each face 6 x 6 = 36 cubes that are painted with one colour.
    Case (i): When red and blue are opposite to each other then from one face we will get 6 x 6 = 36 cubes bot out of them 2 x 6 cubes from common edge with green painted face is common so number of cubes are 2 x 6 x 6 - 2 x 6 = 60
    Case (ii): When red and blue are adjacent to each other then green is either adjacent to these or opposite to any one of red or blue, in 1st st condition number of cubes is 2 x 6 x 6 - 2 x 6 - 11 = 55 cubes or in 2nd condition 2 x 6 x 6 -6 - 6 = 60, required number of cubes is 55 or 60

    Correct Option: C

    Here on each face 6 x 6 = 36 cubes that are painted with one colour.
    Case (i): When red and blue are opposite to each other then from one face we will get 6 x 6 = 36 cubes bot out of them 2 x 6 cubes from common edge with green painted face is common so number of cubes are 2 x 6 x 6 - 2 x 6 = 60
    Case (ii): When red and blue are adjacent to each other then green is either adjacent to these or opposite to any one of red or blue, in 1st condition number of cubes is 2 x 6 x 6 - 2 x 6 - 11 = 55 cubes or in 2nd condition 2 x 6 x 6 -6 - 6 = 60, required number of cubes is 55 or 60

Direction: 125 cubes of similar size are arranged in the form of the bigger cube (5 cubes on each side, i.e., 5 x 5 x 5) All the small cubes lying on the edge of the top layer of the bigger cube are removed and also cubes lying at the four corners of the bottom face are removed. All exposed faces of the block thus left are coloured red.

  1. How many cubes are with two faces painted?








  1. View Hint View Answer Discuss in Forum

    Number of cubes with two face painted from the top side (Which is a square of 3 x 3 = 9 cubes ) is 4.
    Number of cubes with two face painted from the 2nd from top side (Which has four edges and edge has 3 such cubes) is 4 x 3 = 12.
    Number of such cubes from vertical edges is 4 x 1 = 4
    Number of such cubes from bottom face is 4 x 1 = 4
    Hence total such cubes is 4 + 12 + 4 + 4 = 24

    Correct Option: B

    Number of cubes with two face painted from the top side (Which is a square of 3 x 3 = 9 cubes ) is 4.
    Number of cubes with two face painted from the 2nd from top side (Which has four edges and edge has 3 such cubes) is 4 x 3 = 12.
    Number of such cubes from vertical edges is 4 x 1 = 4
    Number of such cubes from bottom face is 4 x 1 = 4
    Hence total such cubes is 4 + 12 + 4 + 4 = 24

  1. How many cubes have three red faces each?








  1. View Hint View Answer Discuss in Forum

    Number of cubes with three coloured face on the top side = 4
    Number of cubes with three coloured face on the 2nd from top side = 4
    Number of cubes with three coloured face on the bottom side = 12
    Total number of such cubes = 12 + 8 = 20

    Correct Option: A

    Number of cubes with three coloured face on the top side = 4
    Number of cubes with three coloured face on the 2nd from top side = 4
    Number of cubes with three coloured face on the bottom side = 12
    Total number of such cubes = 12 + 8 = 20