Question

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

• A. 7.8 m
• B. 9.2 m
• C. 8.3 m
• D. 6.9 m

Answer 1

The correct option is A 7.8 m

Let the length of one side = $x$
$\therefore$ Volume of the cube = $x^3$

Given,
Volume of the cubical box = $474.552{\text{m}}^3$

$\therefore x^3=474.552m^3$
$\Rightarrow x=\sqrt[3]{3474.552}=\sqrt[3]{3\frac{474552}{1000}}$

Prime factorization of 474552:
$\begin{array}{cc}2& 474552\\ 2& 237276\\ 2& 118638\\ 3& 59319\\ 3& 19773\\ 3& 6591\\ 13& 2197\\ 13& 169\\ 13& 13\\ & 1\end{array}$

Prime factorization of 1000:
$\begin{array}{cc}2& 1000\\ 2& 500\\ 2& 250\\ 5& 125\\ 5& 25\\ 5& 5\\ & 1\end{array}$

$\Rightarrow x=\sqrt[3]{3\frac{2\times 2\times 2\times 3\times 3\times 3\times 13\times 13\times 13}{2\times 2\times 2\times 5\times 5\times 5}}$
$=\sqrt[3]{3\frac{3^3\times {13}^3}{5^3}}$
[By cancelling common terms]
$=\frac{3\times 13}{5}$
$=7.8\text{m}$
$\therefore$ Length of the cubical box = 7.8 m