Answer  Hint: The given problem is easy if you have some imagination of cubes. For example, Rubik’s cube has alignment \[3 \times 3 \times 3\]. In Rubik’s cube if you count the number of cubes you will find 27 cubes of equal size. That is exactly the case in our problem. We need to find the number cubes painted on one side only. Complete step-by-step answer: Given, a cube is painted yellow on all six faces and then the cube cuts into 27 small cubes of equal part. So it has been cut into an \[3 \times 3 \times 3\] arrangement. The image that comes to mind is a Rubik’s cube.There is 1 cube in every centre (middle of 3in each axis direction i.e., longitudinal lateral and vertical) which has no colour. On each of the 6 sides of the cube, there is a central smaller cube that is painted on one face.There are 8 corners of the cube, which are painted on 3 surfaces.Remaining 12 cubes are painted on 2 sides only.Thus, only 6 sides of the cube are painted on one face.So, the correct answer is “Option B”. Note: In cube all sides are equal. 12 cubes are painted on 2 sides because on each side of the cube, there are 4 cubes at the middle of the edges. These are shared with one other side of the cube. A cube has 6 faces, 8 vertices and 12 edges. Imagine a cube and follow the explanation which is done above.
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Given: A cube that has been applied 13 cuts. Concept: By cutting the cube for the first time, it will be divided into 2 parts. By cutting the cube along the perpendicular, it will be divided into 4 parts. Again, by cutting the cube along the perpendicular, it will be divided into 8 parts. ⇒ With 3 cuts, there will be a total of 8 cubes. ⇒ It can be concluded that 'n' cuts made along one plane will have 'n + 1' pieces. Calculation: To obtain equal pieces, cuts must be made parallel to 3 planes. Let's assume, a, b, and c cut made along three planes such that there will be (a + 1)(b + 1)(c + 1) = m pieces & a + b + c = 13. ⇒ Several combinations can be made but 'm' will be maximum in (4, 4, 5) cuts. ∴ The required number of pieces = m = (4 + 1)(4 + 1)(5 + 1) ⇒ 5 × 5 × 6 ⇒ 150 India’s #1 Learning Platform Start Complete Exam Preparation
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What is the maximum number of cuts that should be made on the cube to get 91 small cubes or pieces
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