Volumes Practice Test 3

The sphere can be completely fitted in the cube. It means side of the cube is equal to the diameter of the sphere.
Volume of the sphere = $\frac{4}{3}\mathit{\pi }{\left(\mathit{r}\right)}^3$
And volume of the cube = ${\left(\mathrm{side}\right)}^3$
∴ Ratio of the volumes of the cube and the sphere = ${\left(\mathrm{side}\right)}^2:\frac{4}{3}\mathit{\pi }{\mathit{r}}^3$
⇒ ${\left(2\mathit{r}\right)}^3:\frac{4}{3}\mathit{\pi }{\mathit{r}}^3$ = 6 : $\frac{22}{7}$ = 21 : 11