Question
Find the side of a cube whose volume is $\frac{24389}{216}\text{m}^3.$
✓
Answer
Volume of a cube with side s is given by: $\text{V}=\text{s}^3$
$\therefore\text{s}=\sqrt[3]{\text{V}}$
$=\sqrt[3]{\frac{24389}{216}}$
$=\frac{\sqrt[3]{24389}}{\sqrt[3]{216}}$
$=\frac{\sqrt[3]{29\times29\times29}}{\sqrt[3]{2\times2\times2\times3\times3\times3}}$ (By prime factorisation) $=\frac{29}{2\times3}$
$=\frac{29}{6}$ Thus, the length of the side is $=\frac{29}{6}\text{m.}$
$\therefore\text{s}=\sqrt[3]{\text{V}}$
$=\sqrt[3]{\frac{24389}{216}}$
$=\frac{\sqrt[3]{24389}}{\sqrt[3]{216}}$
$=\frac{\sqrt[3]{29\times29\times29}}{\sqrt[3]{2\times2\times2\times3\times3\times3}}$ (By prime factorisation) $=\frac{29}{2\times3}$
$=\frac{29}{6}$ Thus, the length of the side is $=\frac{29}{6}\text{m.}$
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