Question

Find the measurement of the side of a cubical box with volume 2744 cm³.

Note: Numbers on slider are in cm.

• A. 14

Answer 1

The correct option is A 14
$\text{Let the side of cube be x cm.}$
$\text{Given that volume =}{x}^3=2744c{m}^3$

By prime factorizing 2744 you get,
$\begin{array}{cc}2& 2744\\ 2& 1372\\ 2& 686\\ 7& 343\\ 7& 49\\ 7& 7\\ & 1\end{array}$

$2744=2\times 2\times 2\times 7\times 7\times 7=2^3\times 7^3$

$\therefore x=\sqrt[3]{32744}=\sqrt[3]{32^3\times 7^3}x=2\times 7=14$

So, the side of the cubical box is 14 cm.