Question

The volume of a cubical box is 474.552 cubic metres. Find the length of each side of the box.

Answer 1

Volume of a cube is given by:
$V=s^3$, where s = side of the cube

Now
$$\begin{gathered} s^3=474.552cubicmetres \\ \Rightarrow s=\sqrt[3]{474.552}=\sqrt[3]{\frac{474552}{1000}}=\frac{\sqrt[3]{474552}}{\sqrt[3]{1000}} \end{gathered}$$

To find the cube root of 474552, we need to proceed as follows:

On factorising 474552 into prime factors, we get:
$474552=2\times 2\times 2\times 3\times 3\times 3\times 13\times 13\times 13$

On grouping the factors in triples of equal factors, we get:
$474552=\left\{2\times 2\times 2\right\}\times \left\{3\times 3\times 3\right\}\times \left\{13\times 13\times 13\right\}$

Now, taking one factor from each triple, we get:

$\sqrt[3]{474552}=\sqrt[3]{\left\{2\times 2\times 2\right\}\times \left\{3\times 3\times 3\right\}\times \left\{13\times 13\times 13\right\}}=2\times 3\times 13=78$

Also

$\sqrt[3]{1000}=10$


$\therefore$ $s=\frac{\sqrt[3]{474552}}{\sqrt[3]{1000}}=\frac{78}{10}=7.8$

Thus, the length of the side is 7.8 m.