Question

The perimeter of one face of a cube is 24 cm. Find the volume of the cube $\left( \text{in c}{{\text{m}}^{3}} \right)$.

Answer 1

Hint: Here, we will assume the length of the side of the cube to be equal to ‘a’. After this we will try to calculate the value of a by using the value of the perimeter of one of its faces. The volume of the cube will be given as ${{a}^{3}}$, that is, the cube of the length of its side.

Complete step-by-step answer:

In geometry, a cube is a three dimensional solid object bounded by six square faces. At each vertex of the cube, three sides meet.
We know that each of the forces of a cube is a square and the perimeter of a square is given as:
$Perimeter=4\times side$
Since, we have assumed here that the length of one side of the cube is ‘a’ units. Therefore, the perimeter of one face of the cube is = 4a.
Also, it is given that the perimeter is = 24 cm.
So, we can write:
$\begin{align}
  & 4a=24cm \\
 & \Rightarrow a=\dfrac{24}{4}cm \\
 & \Rightarrow a=6cm \\
\end{align}$
So, the length of each of the sides of the cube is equal to 6 cm.
Now, we know that the volume of a cube is given as:
$Vol={{\left( side \right)}^{3}}$
We have already found that the length of the side of the cube is 6 cm. Therefore, the volume of the cube will be:
$Vol={{\left( 6cm \right)}^{3}}=216c{{m}^{3}}$
Hence, the volume of the given cube is $216c{{m}^{3}}$.

Note: Students should note here that each of the faces of a cube is in the form of a square and hence we can use the formula of perimeter of a square to find the length of each side of the given cube. Students should also remember the correct formula for the volume of a cube to avoid mistakes.