Question

A cube of side \[6{\text{ }}cm\] is into number of cubes of side \[2{\text{ }}cm.\] The number of cubes will be
\[\begin{array}{*{20}{l}}
  {A){\text{ }}6} \\
  {B){\text{ }}9} \\
  {C){\text{ }}12} \\
  {D){\text{ }}27}
\end{array}\]

Answer 1

Hint: To solve this question, first we need to find the volume of the bigger cube and then equate that with the volume of the small cube, by using the given sides.

Complete step-by-step answer:
Step 1: We have been given the side of bigger cube \[ = {\text{ }}6{\text{ }}cm\]

So, the volume of bigger cube \[ = {\text{ }}{\left( {side} \right)^3} = {\text{ }}{\left( 6 \right)^3} = {\text{ }}216\]
Also, we have been given side of each small cubes formed from bigger cube \[ = {\text{ }}2{\text{ }}cm\]

So, the volume of small cube \[ = {\text{ }}{\left( {side} \right)^3} = {\text{ }}{\left( 2 \right)^3} = {\text{ }}8\]
Step 2: Now, let the number of small cubes formed from bigger cube be x
To get the number of cubes formed, we will used the formula below mentioned,
Volume of big cube \[ = \] Number of cubes (Volume of smaller cube)
\[216{\text{ }} = {\text{ }}x{\text{ }}\left( 8 \right)\]
\[x\]\[ = \frac{{216}}{8} = 27\]
Thus, number of cubes formed is \[27.\]
So, the correct answer is “Option D”.

Note: Here, students should notice that both the volumes (of bigger cube and small cube) are equal, because we have assumed that no wastage has happened, after cutting the bigger cube into smaller ones.