Question

Find the side of a cube whose volume is $\frac{24389}{216}{\mathrm{m}}^3.$

Answer 1

Volume of a cube with side s is given by:
$V=s^3$

$$\begin{gathered} \therefore s=\sqrt[3]{V} \\ =\sqrt[3]{\frac{24389}{216}} \\ =\frac{\sqrt[3]{24389}}{\sqrt[3]{216}} \end{gathered}$$

$=\frac{\sqrt[3]{29\times 29\times 29}}{\sqrt[3]{2\times 2\times 2\times 3\times 3\times 3}}$ (By prime factorisation)

$$\begin{gathered} =\frac{29}{2\times 3} \\ =\frac{29}{6} \end{gathered}$$

Thus, the length of the side is $\frac{29}{6}\text{m}$.