Cube & Dice Questions with Solutions

17 questions11 easy6 medium

Cube and dice questions test visualisation. Dice questions show one or more positions of a die and ask which number or symbol is opposite a given face. Cube questions describe a large painted cube cut into smaller identical cubes and ask how many small cubes have paint on three, two, one or no faces. For dice, if two positions share a common face, the faces in the same position relative to it are opposite each other. Faces that appear together in any single view can never be opposite. For a painted cube cut into n x n x n small cubes, 8 have three painted faces, 12(n - 2) have two, 6(n - 2)^2 have one, and (n - 2)^3 have none. These formulas solve most cube questions instantly. Practise the cube and dice questions below, each with a step-by-step solution.

All Questions Easy Medium Hard

Q1.
A cube painted red on all its faces is cut into 64 identical smaller cubes. How many of the smaller cubes have exactly two faces painted?
A. 8B. 16C. 24D. 32
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Q2.
A cube painted on all its faces is cut into 125 identical smaller cubes. How many of the smaller cubes have no face painted?
A. 27B. 36C. 54D. 64
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Q3.
A cube painted on all its faces is cut into 27 identical smaller cubes. How many of the smaller cubes have at least one face painted?
A. 8B. 20C. 26D. 27
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Q4.
Three different positions of the same dice are shown below. Which number is on the face opposite to 2?
A. 1B. 3C. 4D. 6
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Q5.
Two positions of the same dice are shown below. Which number is on the face opposite to 5?
A. 1B. 2C. 4D. 6
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Q6.
A cube is painted on all its six faces with different colors. The cube is then cut into 64 smaller cubes of equal size. How many of the smaller cubes will have exactly two painted faces?
A. 12B. 16C. 24D. 32
easyAsked in MAH LLB 3 Year CET 2 April Shift-2 2026View solution ›
Q7.
A cube painted red on all faces is cut into 64 equal smaller cubes. How many of the smaller cubes have no face painted?
A. 16B. 0C. 8D. 24
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Q8.
A cube painted on all faces is cut into 125 equal smaller cubes. How many of the smaller cubes have only one face painted?
A. 36B. 54C. 48D. 27
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Q9.
Directions (Q16–Q17): Two different positions of the same dice are shown below. Study them and answer the question. Which number is on the face opposite to 1?
A. 4B. 5C. 6D. 3
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Q10.
Directions (Q16–Q17): Two different positions of the same dice are shown below. Study them and answer the question. Which number is on the face opposite to 3?
A. 2B. 4C. 6D. 5
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Q11.
A cube painted red on all its faces is cut into 64 identical smaller cubes. How many of the smaller cubes have no face painted?
A. 8B. 16C. 24D. 27
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Q12.
A cube painted on all its faces is cut into 125 identical smaller cubes. How many of the smaller cubes have exactly one face painted?
A. 36B. 54C. 48D. 27
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Q13.
Two different positions of the same dice are shown below. Which number is opposite 3?
A. 5B. 1C. 6D. 2
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Q14.
Three different positions of the same dice are shown below. Which letter is opposite A?
A. BB. EC. CD. D
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Q15.
A cuboid $4 c m \times 3 c m \times 2 c m$ , painted on all its faces, is cut into cubes of side $1 c m$ . How many of these cubes have no face painted?
A. 2B. 0C. 4D. 6
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Q16.
How many minimum numbers of colours will be required to paint all the sides of a cube without the adjacent sides having the same colours?
A. 3B. 4C. 5D. 6
easyAsked in NIMCET 2020 +1View solution ›
Q17.
A cube is made up of 125 one cm cubes and placed on a table. How many small cubes are visible on exactly three sides?
A. 4B. 8C. 12D. 16
mediumAsked in NIMCET 2017View solution ›