Question

32. A cube of side 6 cm is in a number of bes each of side 2. The number of cubes forme is.
A.6
B.9
C.12
D.27 ​

Answer 1

Answer :-

• Option d) is correct.

• 27 cubes are formed.

To find :-

• The number of cubes formed.

Step-by-step explanation :-

 

Here, it is given that :-

• Side of the larger cube = 6 cm.

• Side of the smaller cube = 2 cm.

Let's find the volume of the larger and smaller cube!

We know that :-

$\underline{\boxed{\sf{Volume \: of \: a \: cube = {(Side)}^{3}}}}$

Therefore, the volume of the larger cube is :

$\longrightarrow \: \sf{{(Side)}^{3}}$

$\longrightarrow \: \sf{{(6)}^{3}}$

$\longrightarrow \: \sf{6 \times 6 \times 6}$

$\longrightarrow \: \sf{216 \:{cm}^{3}}$

And the volume of the smaller cube is :

$\longrightarrow \: \sf{{(Side)}^{3}}$

$\longrightarrow \: \sf{{(2)}^{3}}$

$\longrightarrow \: \sf{2 \times 2 \times 2}$

$\longrightarrow \: \sf{8 {cm}^{3}}$

Now,

$\underline{ \boxed{\sf{No. \: of\: cubes = \dfrac{Volume \: of \: larger \: cube}{Volume \: of \: smaller \: cube}}}}$

Here,

• Volume of the smaller cube = 8 cm³.
• Volume of the larger cube = 216 cm³.

Therefore,

$\longrightarrow \: \sf{No. \: of \: cubes = \cancel{\dfrac{216}{8}}}$

 

$\longrightarrow \: \sf{27 \: cubes.}$

Hence :-

• 27 cubes are formed.

• Option d) is correct.

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