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The volume of a cubical box is 474.552 cubic metres. Find the length of each side of the box.
Given:
The volume of a cubical box is 474.552 cubic metres.
To find:
We have to find the length of each side of the box.
Solution:
The volume of thr cubical box $=474.552 \mathrm{cu} \mathrm{m}$
Therefore,
Length of each side $=\sqrt[3]{\text { Volume }}$
$=\sqrt[3]{474.552}$
$=\sqrt[3]{\frac{474552}{1000}}$
$=\frac{\sqrt[3]{474552}}{\sqrt[3]{1000}}$
Prime factorisation of 474552 is,
$474552=2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 13 \times 13 \times 13$
This implies,
$\frac{\sqrt[3]{474552}}{\sqrt[3]{1000}}=\frac{\sqrt[3]{2 \times 2 \times 2 \times 3 \times 3 \times 3 \times 13 \times 13 \times 13}}{\sqrt[3]{10 \times 10 \times 10}}$
$=\frac{\sqrt[3]{2^{3} \times 3^{3} \times 13^{3}}}{\sqrt[3]{10^{3}}}$
$=\frac{2 \times 3 \times 13}{10}$
$=\frac{78}{10}$
$=7.8 \mathrm{~m}$
The length of each side of the box is $7.8\ m$.