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Determine the ratio of the volume of a cube to that of the sphere which will exactly fit inside the cube.
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Let the side of the cube be '$x$' units
$\therefore$ Radius of the sphere = $\frac{x}{2}$ units
$$\begin{aligned}& \frac{\text{Volume of cube}}{\text{Volume of sphere}} = \frac{x^3}{\frac{4}{3}\pi \times (\frac{x}{2})^3} \\ & = \frac{6}{\pi} \\ & \therefore\end{aligned}$$ required ratio is $6 : \pi$
$\therefore$ Radius of the sphere = $\frac{x}{2}$ units
$$\begin{aligned}& \frac{\text{Volume of cube}}{\text{Volume of sphere}} = \frac{x^3}{\frac{4}{3}\pi \times (\frac{x}{2})^3} \\ & = \frac{6}{\pi} \\ & \therefore\end{aligned}$$ required ratio is $6 : \pi$