Question

A cube of side 6 cm is cut into number of cubes each of side 2cm.the number of cubes formed are​

Answer 1

Correct Question:

A cube of side 6 cm is cut into number of cubes each of side 2cm.the number of cubes formed are

Answer :

Total number of cubes is 72 .

Solution :

Step 1 : First , we will find the cube before cutting them in the pieces .

$\implies\sf{volume \: = 6 {}^{3} = 216.}$

Step 2 : We will find side of cube which is formed of 6cm = 2cm .

$\implies\sf{volume \: = 2 {}^{3} = 8}$

Step 3. Now, we have to find the number of cubes which are formed

So let us Take the number of cubes formed = N

See there is no wastage.

Step 4 : Now we will find the , Volume of bigger volume is equal to volume of smaller cubes.

$\implies\sf{216 = n \times 8}$

$\implies\sf{n = \frac{216}{8} = 27 }$

Hence, Number of cube formed from the bigger cube = 27.

Answer 2

Given that ,

A cube of side 6 cm is cut into number of cubes each of side 2 cm

We know that , the volume of cube is given by

$\large \sf\fbox{Volume = {(side)}^{2} }$

Thus , the volume of cube whose side is 6 cm will be

$\sf \mapsto Volume = {(6)}^{3} \\ \\ \sf \mapsto Volume = 216 \: \: {m}^{3}$

Now , the volume of cube whose side is 2 cm will be

$\sf \mapsto Volume = {(2)}^{3} \\ \\ \sf \mapsto Volume = 8 \: \: {m}^{3}$

According to the question ,

$\sf\fbox{Volume \: of \: big \: cube = n × Volume \: of \: small \: cube}$

Where ,

n = number of cubes

Thus ,

$\sf \mapsto n = \frac{216}{8} \\ \\ \sf \mapsto n = 27$

$\sf \therefore \underline{The \: number \: of \: cubes \: formed \: is \: 27}$