a cube is cut parallele to one face by making 8 cuts such that all the resulting pieces are identical.what is the max num of identical pieces thet can be obtained by making 9 more cuts in any direction?
Answers
Given:
A cube - 6 sides.
Cut parallel to once face by making 8 cuts
Identical pieces.
To find:
The maximum number of identical pieces that can be obtained now by making 9 more cuts in any direction.
Solution :
The ways in which the cube can be cut parallel to one fact to obtain identical pieces are,
Consider the cube having faces,
Front ABCD
Back PQRS
The cube is already cut 8 times and can be cut two or more times to make identical pieces.
9 more cuts can be made.
As we know, all the sides are same in a cube.
We can obtain triangular shaped identical pieces by making 9 cuts along faces AC and BD. This will result in, 8 * 4 = 32 pieces. Here, all the pieces are identical.
We can obtain square shaped identical pieces by making 9 cuts along the faces PQ and RS. This will result in 8 * 4 = 32 pieces. Here, all the pieces are identical.
There are other ways in which the cube can be cut but, it will not result in identical pieces.
Hence, 32 identical shaped pieces can be obtained by making 2 more cuts in any direction.
A cube is similar to all sides, but when cut internally or diagonally, it tends to change its shape and size.
Hence, if the cube here as per the questions, cut in 8 shapes, all the resulting shapes are identical, then it is undoubtedly a proper cube from all sides.
But this does not ensure if the cut is made in any other direction, the cube will result in the same similar shapes.