Question

A cube is cut parallel to one face by making 10 cuts what is the maximum number of identical pieces that can be obtained

Answer 1

The maximum number of identical pieces that can be obtained from cube is 80

Solution:

Given, a cube is cut parallel to one face by making 10 cuts  

We have to find what is maximum number of identical pieces that can be obtained

A cube - 6 sides.

In order to get maximum number of pieces with given number of cuts, divide the total cuts equally among the three axis.  

But here we have cut 10 times, we cannot distribute equally among all the three axis.  

In such case, to maximize the total number of pieces, we need to minimize the difference between the number of cuts in any two axis is minimum.  

For 10 cuts, we can divide it as x = 3, y = 3, z = 4.  

Any other combination of numbers will result in a lower number of pieces.  

So, now, maximum number of pieces is (3 + 1)(3 + 1)(4 + 1) = 4 x 4 x 5 = 80  

Hence, we can get maximum of 80 identical pieces.

Answer 2

Answer:

A cube is cut parallel to one face by making 10 cuts such that all the resulting pieces are identical. What is the maximum number of identical pieces that can be obtained now by making 3 more cuts in any direction.

Step-by-step explanation:

A cube is cut parallel to one face by making 10 cuts such that all the resulting pieces are identical. What is the maximum number of identical pieces that can be obtained now by making 3 more cuts in any direction.