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.