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

AcademicMathematicsNCERTClass 8

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 $7.8\ m$.

raja
Updated on 10-Oct-2022 12:47:42

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