Cube & Dice Questions with Solutions
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.
- 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. 32easyView solution › - 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. 64easyView solution › - 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. 27easyView solution › - Q4.
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. 32easyAsked in MAH LLB 3 Year CET 2 April Shift-2 2026View solution › - Q5.
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. 24easyView solution › - Q6.
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. 27easyView solution › - Q7.
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. 3easyView solution › - Q8.
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. 27easyView solution › - Q9.
Two different positions of the same dice are shown below. Which number is opposite 3?
A. 5B. 1C. 6D. 2easyView solution › - Q10.
Three different positions of the same dice are shown below. Which letter is opposite A?
A. BB. EC. CD. DeasyView solution › - Q11.
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. 6easyAsked in NIMCET 2020 +1View solution ›