The volume of a cubical box is 474. 552 cubic metres. Find the length

1.	The volume of a cubical box is 474. 552 cubic metres. Find the length of each side of the box.
Answer» Given, Volume of a cube = 474.552 cubic metres V = 8³, S = side of the cube So, 8³ = 474.552 cubic metres = 8 = \(\sqrt[3]{474.552}\) = \(\sqrt[3]{\frac{474552}{1000}}\) = \(\frac{\sqrt[3]{474552}}{\sqrt[3]{1000}}\) On factorising 474552 into prime factors, we get: 474552 = 2×2×2×3×3×3×13×13×13 On grouping the factors in triples of equal factors, we get: 474552 = {2×2×2}×{3×3×3}×{13×13×13} Now taking 1 factor from each group we get: \(\sqrt[3]{474.552}\) = \(\sqrt[3]{{\{2\times2\times2\times\}}\{\times3\times3\times3\}\{13\times13\times13\}}\) = \(2\times3\times13\) = 78 Also, \(\sqrt[3]{1000} = 10\) ∴ \(8 = \frac{\sqrt[3]{474552}}{\sqrt[3]{1000}}\) = \(\frac{78}{10} = 7.8\) So, length of the side is 7.8m.

The volume of a cubical box is 474. 552 cubic metres. Find the length of each side of the box.

Answer»

Given,

Volume of a cube = 474.552 cubic metres

V = 8³,

S = side of the cube

So,

8³ = 474.552 cubic metres

= 8 = \(\sqrt[3]{474.552}\) = \(\sqrt[3]{\frac{474552}{1000}}\) = \(\frac{\sqrt[3]{474552}}{\sqrt[3]{1000}}\)

On factorising 474552 into prime factors, we get:

474552 = 2×2×2×3×3×3×13×13×13

On grouping the factors in triples of equal factors, we get:

474552 = {2×2×2}×{3×3×3}×{13×13×13}

Now taking 1 factor from each group we get:

\(\sqrt[3]{474.552}\) = \(\sqrt[3]{{\{2\times2\times2\times\}}\{\times3\times3\times3\}\{13\times13\times13\}}\)

= \(2\times3\times13\) = 78

Also,

\(\sqrt[3]{1000} = 10\)

∴ \(8 = \frac{\sqrt[3]{474552}}{\sqrt[3]{1000}}\) = \(\frac{78}{10} = 7.8\)

So, length of the side is 7.8m.