NCERT Class VIII exercise 7.1, problem statement 4

Chapter Name Cubes and Cube Roots

The exercise and problem number in question are 7.1 and 4 respectively, 

Problem Statement, 

Parikshit makes a Cubiod of plastic one of sides 5cm,2cm,5cm. HOW MANY SUCH CUBIODS WILL BE NEED TO FORM A CUBE? 

The Solution taught by the teacher in the school The PSBB millennium school, Gerugambakkam, Chennai is that we require twenty such cubiods, 

A perfect a cube is only possible if the sides are of equal length. For example 1,8,27,64,125, 216,343… and so on are examples of cubes whose sides measure 1,2,3,4,5, 6,7. Respectively.

In my view and understanding we could never make a perfect cube or rubix cube where the dimensions of the each of components sides are not equal.

The solutions is 20 such cubiods forms a non rubix cube of matrix 2,2,5 where 2 row, 2 columns and 5 perpdicular arrangements. That would mean it would be a non rubix cube and not a rubix cube.

Therefore, in my view and understanding the question should clearly state us to form a non rubix cube asking to make a cube out of cubiods is bit confusing as I related a cube to rubix cube where each individual components are cubes themselves. Therfore, the question perhaps should have been to form a non rubix cube from the cubiods of given dimension, where in only the resulting cubes dimensions are of same length, i.e length =breadth =height.

My conclusion is that a non rubix cube can be formed by 20 such cubiods, the Solution is to find the LCM of 5,5,2 which is 10 and the number of cubiods required to form the non rubix cube would simply be, product of (LCM of Length, breadth, height / length *LCM of Length, breadth, height / breadth * LCM of Length, breadth, height / height) = 10/5*10/5*10/2=2*2*5=4*5=20

The smallest number of non rubix cube that can be formed is 20 and the

The resulting non rubix cube would be 3D matrix of 2 rows, 2columns,5 perpendiculars. The resulting objects dimension would be length=10,breadth =10,height=10, the overall volume is 10^3=1000

Therefore, 3 dimensional picture to the solution would be better for understanding and that helps the students.