Question

How many 3 cm cubes can be formed by melting a 15 cm cube of metal?

Answer 1

Hint:
Here, we will first assume the number of cubes to be any variable \[n\] and then we will find the volume of 3 cm cubes and then multiply the value of one small cube by \[n\] to calculate the volume of \[n\] number of cubes. Then we will equate the value of the volume of \[n\] number of cubes with the volume of the cube of sides 15 cm. After equating the value, we will get the number of cubes formed.

Complete step by step solution:
Let the number of cube that can be formed by melting a 15 cm cube of metal be \[n\]
Now, let’s find the value of the cube of sides 3 cm first.
Volume of 3 cm cube\[ = {\left( {3{\rm{cm}}} \right)^3} = 27{\rm{c}}{{\rm{m}}^3}\]
So, to calculate the volume of n number of cubes of sides 3 cm, we will multiply it with n.
Volume of \[n\] number of 3 cm cube \[ = n \times 27{\rm{c}}{{\rm{m}}^3}\] …………..\[\left( 1 \right)\]
Now, volume of cube of sides 15 cm \[ = {\left( {15{\rm{cm}}} \right)^3} = 3375{\rm{c}}{{\rm{m}}^3}\]……………..\[\left( 2 \right)\]
Now, equating equation \[\left( 1 \right)\] with equation \[\left( 2 \right)\] we get;
 \[3375{\rm{c}}{{\rm{m}}^3} = n \times 27{\rm{c}}{{\rm{m}}^3}\]
Now, dividing 3375 by 27, we get
\[\Rightarrow n = \dfrac{{3375{\rm{c}}{{\rm{m}}^3}}}{{27{\rm{c}}{{\rm{m}}^3}}}\]
\[\Rightarrow n = 125\]

So, the required number of 3 cm cubes that can be formed by melting a 15 cm cube of metal is 125.

Note:
Since we have used volume of a cube, where volume is the measurement of space available in a particular object in cubic units.
We can solve this question by using formula i.e.
Number of smaller cubes formed\[ = \] volume of larger cubes/ volume of smaller cubes\[\]
Volume of 3 cm cube\[ = {\left( {3{\rm{cm}}} \right)^3} = 27{\rm{c}}{{\rm{m}}^3}\]
Now, Now, volume of cube of sides 15 cm \[ = {\left( {15{\rm{cm}}} \right)^3} = 3375{\rm{c}}{{\rm{m}}^3}\]
So, substituting the volume of 3cm cube and 15 cm cube in the formula for number of cubes, we get
Number of smaller cubes formed\[ = \dfrac{{3375}}{{27}} = 125\]
So the number of 3cm cubes that can be formed is 125.