Question Bank - Cubes


  • IIM Lucknow | MathOratory


    Number of Questions : 18
    Topic : Cubes
    Answer key available ? : Yes
    Source : MathOratory team.


  • IIM Lucknow | MathOratory


    Q1) What will be the maximum number of pieces generated if a cube is cut 6 times, each cut being parallel to some surface?

    Ans - 27


  • IIM Lucknow | MathOratory


    Q2) What will be the maximum number of pieces generated if a cube is cut 6 times, each cut parallel to some surface, if after every cut you are allowed to reorder the cut out pieces ?

    Ans : 64


  • IIM Lucknow | MathOratory


    Q3) You have a cube which is made up of 1331 identical smaller cube. You make two straight cuts through the cube, diagonal to the same face. Find the maximum number of small cubes cut.

    Ans - 231


  • IIM Lucknow | MathOratory


    Q4) A cube of side length 20 cm is taken. Another cube of side length 5 cm is cut off from the bigger cube. What is the percentage change in the surface area of the large cube?
    a. 0%
    b. 1.5625%
    c. 3.25%
    d. Data Insufficient

    Ans - d


  • IIM Lucknow | MathOratory


    Q5) A cube is kept on top of a desk and then coloured on all of its exposed surfaces. If the cube consists of 125 identical smaller cubes, how many small cubes are coloured on exactly one surface?

    Ans - 57


  • IIM Lucknow | MathOratory


    Q6) A cube is kept on top of a desk and then coloured on all of its exposed surfaces. If the cube consists of 125 identical smaller cubes, how many small cubes are coloured on exactly one surface?

    Ans - 36


  • IIM Lucknow | MathOratory


    Q7) A cube is kept on top of a desk and then coloured on all of its exposed surfaces. If the cube consists of 125 identical smaller cubes, how many small cubes are coloured on 2 surfaces?

    Ans - 28


  • IIM Lucknow | MathOratory


    Q 8 ) A cube is kept at the edge of a room and then coloured on all of its exposed surfaces. If the cube consists of 125 identical smaller cubes, how many small cubes are coloured on 2 surfaces?

    Ans - 19


  • IIM Lucknow | MathOratory


    Q 9) A cube is kept at the corner of a room and then coloured on all of its exposed surfaces. If the cube consists of 125 identical smaller cubes, how many small cubes are coloured on 1 surfaces?

    Ans - 48


  • IIM Lucknow | MathOratory


    Q 10) A cuboid made up of 336 small identical cubes, such that the dimension of the cuboid in terms of the cubes is 6x7x8, is kept at the corner of a room and coloured on its exposed surfaces. Find the maximum number of small cubes coloured on 2 surfaces.

    Ans - 18


  • IIM Lucknow | MathOratory


    Q 11) A cube is made up of 125 identical smaller cubes. It is painted with red, green and blue colours in such a way that 3 pairs of adjacent surfaces are painted with the same colour. How many cubes have 3 colours on them?

    Ans - 2


  • IIM Lucknow | MathOratory


    Q 12) A cube is made up of 125 identical smaller cubes. It is painted with red, green and blue colours in such a way that 3 pairs of adjacent surfaces are painted with the same colour. How many cubes have 2 colours on them?

    Ans - 33


  • IIM Lucknow | MathOratory


    Q 13) A cube is made up of 125 identical smaller cubes. It is painted with red, green and blue colours in such a way that 3 pairs of adjacent surfaces are painted with the same colour. How many cubes have 2 faces painted with the same colour?

    Ans - 15


  • IIM Lucknow | MathOratory


    Q 14) A cube is made up of 125 identical smaller cubes. It is painted with red, green and blue colours in such a way that 3 pairs of adjacent surfaces are painted with the same colour. How many cubes have only red and blue colour on them?

    Ans - 11


  • IIM Lucknow | MathOratory


    Q 15) A cube is made up of 125 identical smaller cubes. It is painted with red, green and blue colours in such a way that 3 pairs of adjacent surfaces are painted with the same colour. How many cubes have red or blue colour on them?

    Ans - 77


  • IIM Lucknow | MathOratory


    Q 16) A cube is cut into 27 identical cubes, where re-orienting the pieces are allowed after each cut.
    What is the minimum number of cuts required ?

    Ans - 6


  • IIM Lucknow | MathOratory


    Q 17) A cube made up of 1331 identical smaller cubes is placed at the edge of the room.
    Minimum how many such small cubes are required to cover this cube entirely?
    Further Details: By covering we mean, nothing of the earlier cube must be visible. No edge, no corner, no face

    Ans - 541


  • IIM Lucknow | MathOratory


    Q 18) 729 identical cubes are painted black and put together to form 27 identical medium sized cubes. These medium sized cubes are repainted red on its exposed surfaces and put together to form 1 large cube. This large cube is again repainted black on its exposed surfaces. How many of the initial small cubes have now only black colour on them?

    Ans - 125


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