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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Updated on: 10-Oct-2022

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