Question

The volume of a cubical box is $474.552$ cubic meters. Find the length of each side of the box.​

Answer 1

Given : Volume of a cube $=474.552m^3$

Let the sides of the cube be a

$\therefore \text{Volume of the cube}=a^3$
$\because a^3=474.552=\frac{474552}{1000}$
$\therefore a=\sqrt[3]{3\frac{474552}{1000}}$

$=\frac{\sqrt[3]{3472552}}{\sqrt[3]{31000}}$ $[\because \sqrt[3]{3\frac{a}{b}}=\frac{\sqrt[3]{3a}}{\sqrt[3]{3b}}]$

$\frac{\sqrt[3]{32\times 2\times 2\times 3\times 3\times 3\times 13\times 13\times 13}}{\sqrt[3]{310\times 10\times 10}}$
$=\frac{2\times 3\times 13}{100}$
$=\frac{78}{10}=7.8m$

Hence, the side of the cube is $7.8m$