Question

A cube is cut parallel to one face by making 12 cuts such that all the resulting pieces are identical. What is the maximum number of identical pieces that can be obtained now by making 2 more cuts in any direction?

Answer 1

Answer:

Maximum number of identical pieces = 48

Step-by-step explanation:

The figure associated with answer shows the resulting cube .

The cube is cut parallel to one face by making 12 cuts such that all the resulting pieces are identical.

We can make maximum number of identical pieces that can be obtained in two ways.

1) Cut the cube along AC and BD  we get 12 x 4 =48 triangular shaped identical pieces.

2) Cut the cube along PQ and RS  we get 12 x 4 =48 square shaped identical pieces.

So these are the two method  to get maximum number of identical pieces

Answer 2

Given:

A cube - 6 sides.

Cut parallel to once face by making 12 cuts

Identical pieces.

To find:

The maximum number of identical pieces that can be obtained now by making 2 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 12 times and can be cut two or more times to make identical pieces.

Two cuts can be made.

As we know, all the sides are same in a cube.

• We can obtain triangular shaped identical pieces by making 12 cuts along faces AC and BD. This will result in, 12 * 4 = 48 pieces. Here, all the pieces are identical.
• We can obtain square shaped identical pieces by making 12 cuts along the faces PQ and RS. This will result in 12 * 4 = 48. 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, 48 identical shaped pieces can be obtained by making 2 more cuts in any direction.