A cube which is painted red on all its sides is cut into 27 small cubes now how many cubes have 3 red faces
Answers
A painted cube that is cut into 27 equal-size smaller cubes has been cut into a 3 * 3 * 3 arrangement.
There is 1 cube in the very center (middle of 3 in each axis direction -- pitch, roll, and yaw), so 1 cube has no paint .
On each of the 6 sides of the cube, there is a central smaller cube that is painted once.
Also on each of the 6 sides of the cube, there are 4 cubes (at the middle of the edges).
These are shared with one other side of the cube (or we could just count the 12 edge lines -- 12). So, 6 * 4 / 2, or just 12, smaller cubes are painted on 2 edges.
That leaves the 8 corners of the original cube, which are painted on 3 surfaces.
1 (no paint) + 6 (painted 1) + 12 (painted 2) + 8 (painted 3) = 27 total
Concept
A cube is a 3D solid shape that has 6 faces. A cube is one of the simplest shapes in three-dimensional space. All six faces of the cube are squares, a two-dimensional shape.
It has all its faces in a square shape.
All faces or sides have the same dimensions.
The plane angles of a cube are right angles.
Each of the faces meets the other four faces.
Each of the vertices meets three faces and three edges. Opposite edges are parallel.
Given
It is given that a cube is painted red on all its sides is cut into 27 small cubes
Find
We need to need the number of cubes having 3 red faces
Solution
Cube has 8 vertices(Corners)
Vertex is a point where all the three faces meet
Therefore there are 8 cubes which have 3 red faces because there are 8 vertices which meet at a point where all the faces which are red in colour meet each other
Hence there are 8 cubes which have 3 red faces
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