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Cubes made of small cubes – practice for Years 5–7

Sample questions on Cubes made of small cubes with the right answer and a worked solution, from easy to hard. In the Pickles Academy app a child gets new questions of the same kind every time, so they can't just learn the answers by heart.

Subject
Maths
Year
Years 5–7
Curriculum area
Geometry and measures

Question types: The painted cube

Rule: Cubes made of small cubes

A cube with edge n is made of n × n × n small cubes. Three painted faces: only the corners, always 8.

Two faces: edges without corners, 12 × (n − 2). One face: 6 × (n − 2)². None: (n − 2)³.

Example: n = 4: unpainted inside 2 × 2 × 2 = 8

Watch out: “At least one face” = all the small cubes except the unpainted ones inside.

Sample questions

  1. Question 1 Easy

    A big cube with 3 cm edges is glued together from cubes with 1 cm edges, and its whole surface is painted. How many small cubes have exactly three painted faces?

    Show the solution
    Answer: 8

    How it works: Only the corner cubes have three painted faces, and a cube has 8 corners.

  2. Question 2 Normal

    A big cube with 3 cm edges is glued together from cubes with 1 cm edges, and its whole surface is painted. How many small cubes have exactly one painted face?

    Show the solution
    Answer: 6

    How it works: Cubes in the middle of a face have one painted face: 6 faces with 1 × 1 each, so 6 × 1 = 6.

  3. Question 3 Hard

    A big cube with 4 cm edges is glued together from cubes with 1 cm edges, and its whole surface is painted. How many small cubes have at least one painted face?

    Show the solution
    Answer: 56

    How it works: There are 64 cubes in all, 8 unpainted inside: 64 − 8 = 56.

Related topics

All Maths topics

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