If the volume of a sphere is twice that of the other, then the ratio of their radii is :

1. 2 : 1

2. 4 : 1

3. $\sqrt{2}$ : 1

4. $\sqrt[3]{2}$ : 1

Let the radius of sphere 1 be r cm and radius of sphere 2 be R cm.

Volume of sphere = $\dfrac{4}{3}π \times \text{r}^3$

Given,

Volume of sphere 1 = 2 × Volume of sphere 2

$\Rightarrow \dfrac{4}{3}π \times \text{r}^3 = 2 \times \dfrac{4}{3}π \times \text{R}^3 \\[1em] \Rightarrow \text{r}^3 = 2 \times \text{R}^3 \\[1em] \Rightarrow \dfrac{\text{r}^3}{\text{R}^3} = \dfrac{2}{1} \\[1em] \Rightarrow \Big(\dfrac{\text{r}}{\text{R}}\Big)^3 = \dfrac{2}{1} \\[1em] \Rightarrow \dfrac{\text{r}}{\text{R}} = \sqrt[3]{\dfrac{2}{1}} \\[1em] \Rightarrow \dfrac{\text{r}}{\text{R}} = \dfrac{\sqrt[3]{2}}{1}$

Hence, option 4 is the correct option.