Cube is an important topic in the competitive exams because every year asked questions from this topic. Here are the explained different cube problems with solutions from which practices, you can easily solve these type of questions in the competitive exams.
So, continue your practice by given these some cube problems with solutions which will help you to improve your score in the competitive exams. Click here to solve Square Root and Cube Root Problems with Solutions.
A cube is a three-dimensional solid having 6 faces, 12 edges and 8 corners. All the edges of a cubes are equal and hence all the faces are square in shape.
The questions on cubes may belong to anyone of the following categories:
1. A cube is cut by making certain specified number of cuts. The directions in which the cuts are made may or may not be given. We are to find the number of identical pieces resulting out of the given cut.
2. The number of identical pieces, into which a cube is cut, is given and we need to find the number of cuts.
3. A cube could be painted on all or some of its faces with the same colour or different colours and then cut into a certain specified number of identical pieces. The questions of the form- "How many small cubes have 2 faces painted?" "How many smaller cubes have only one face painted?" etc. could then be framed.
To solve the questions related to cubes you should definitely follow the given rules. The given rules help you to memories the shortcuts useful in solving the questions.
lf a cube is painted on all six surfaces and cut into x number of identical cubes then,
1. Number of cubes having no surface pointed = (n - 2)3
2. Number of cubes having one surface painted (n - 2)2 x 6
3. Number of cubes having two surfaces painted (n- 2) x 12.
4. Number of cubes having three surfaces painted = 8
5. There cannot be a cube which has more than three surfaces painted.
Note : - If a cube of side ‘a’ cm is cut into pieces such that each side of the smaller cube is of “b” cm then
Q.1. A cube is cut into two equal parts along a plane parallel to one of its faces. One piece is then coloured red on the two larger faces and green on the remaining while the other is coloured green on two smaller adjacent faces and red on the remaining. Each is then cut into 32 cubes of the same size. The 64 cubes are then mixed up.
1. How many cubes have no coloured face at all?
(A) 16
(B) 8
(C) 4
(D) 0
Q.2. How many cube have only one coloured face?
(A) 8
(B) 16
(C) 20
(D) 24
Q.3. How many cubes have two red and one green face?
(A) 4
(B) 8
(C) 12
(D) 16
Q.4. How many cubes have one face red another green?
(A) 32
(B) 24
(C) 16
(D) 8
Q.5. What is the number of cubes with at least one green face?
(A) 46
(B) 38
(C) 36
(D) 28
If you want to ask anything related cube problems and its solutions, you can ask me in the comment section. Visit on the next page for more practice.
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