Question

the volume of a cubical box is 13.824 cubic metres.find the length of each side of a cube.

Answer 1

it's a question of basic equations in one variable
Let us assume that the side of the cube is l meter as they all are identical.
now ,
for a cube of side l,
volume
${l}^{3} = 13.824 \\ l = \sqrt[3]{13.824 } \\ l = 2.4$
so the length of one side of cube is 2.4 meter

Answer 2

The length of each side of a cube (a) = $\dfrac{24}{10}$ m or, 2.4 m

Step-by-step explanation:

Given,

The volume of a cubical box = 13.824 $m^{3}$

Let each side of a cubical box = a

To find, the length of each side of a cube (a) = ?

We know that,

The volume of a cube = $a^{3}$

∴ $a^{3}$ = 13.824

⇒ $a^{3}$ = $\dfrac{576\times 24}{10\times 10\times 10}$

⇒ $a^{3}$ = $\dfrac{24\times 24\times 24}{10\times 10\times 10}$

⇒ $a^{3}$ = $(\dfrac{24}{10})^2$

⇒ a = $\dfrac{24}{10}$ m

⇒ a = 2.4 m

∴ The length of each side of a cube (a) = $\dfrac{24}{10}$ m or, 2.4 m