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Find side of a cube whose volume is \( \frac{24389}{216} \mathrm{~m}^{3} \).
Given :
The volume of a cube is $\frac{24389}{216}\ m^3$.
To do :
We have to find the side of the cube.
Solution :
Let the side of the given cube be $a\ m$.
We know that,
The volume of a cube of side $a$ is $a^3$.
Therefore,
$a^3= \frac{24389}{216}$
$a^3 = \frac{29\times29\times29}{6\times6\times6}$
$a^3= \displaystyle \frac{29^{3}}{6^{3}}$
$a^3 = (\frac{29}{6})^3$
$\Rightarrow a = \frac{29}{6}$ m.
The length of the side of the cube is $\frac{29}{6}\ m$.
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