Question

find the number of cubes of Side 2 cm which can be cut from a cube of side 6 centimetre​

Answer 1

$\Large {\underline { \sf \orange{Clarification :}}}$

Here, we are given that cubes of side 2 cm are to be cut from a cube of side 6 cm. We have to find out the the number of cubes of side 2 cm which can be cut from a cube of side 6 cm.

In order to solve this question, we'll have to find the volume of one cube of 2 cm and the volume of one cube of 6 cm. We'll assume the number of cubes as a variable. Then, we'll form a linear equation as per the asked question. By solving that equation we'll find the number of cubes required.

$\Large {\underline { \sf \orange{Explication \: of \: Steps :}}}$

Let the number of cubes be x. So,

» Number of cubes × Volume of one cube of side 2 cm is equivalent to the volume of onw cube of 6 cm.

Here,

• Let us denote volume of one cube of side 2 cm as v and,
• Volume of one cube of 6 cm as V.

$\longrightarrow \sf { v \times x = V}$

$\dag$ Finding volume of one cube of side 6 cm(V) :

We know that,

$\bigstar \: \boxed{\sf{ Volume_{(Cube)} = {Side}^{3} }}$

So,

$\longrightarrow \sf { V = {6}^{3} \: {cm}^{3} }$

$\longrightarrow \sf { V = 6 \: cm \times 6 \: cm \times 6 \: cm}$

$\longrightarrow \boxed{\sf { V = 216 \: cm^3 }}$

$\dag$ Finding volume of the cube of side 2 cm(v) :

We know that,

$\bigstar \: \boxed{\sf{ Volume_{(Cube)} = {Side}^{3} }}$

So,

$\longrightarrow \sf { v = {2}^{3} \: {cm}^{3} }$

$\longrightarrow \sf { v = 2 \: cm \times 2 \: cm \times 2 \: cm}$

$\longrightarrow \boxed{\sf { v = 8 \: cm^3 }}$

Substituting values in the equation,

$\longrightarrow \sf { v \times x = V}$

$\longrightarrow \sf { 8 \: cm^3 \times x = 216 \: cm^3}$

$\longrightarrow \sf { x =\cancel{ \dfrac{216 \: cm^3}{8 \: cm^3}} }$

$\longrightarrow \underline{\boxed{\sf{ x = 27 }}} \: \orange{\bigstar}$

Therefore,

• Number of cubes of Side 2 cm which can be cut from a cube of side 6 cm are 27 cubes.