​If $$V_1 , V_2$$ a volumes and $$S_1 ,S_2$$  are the surface areas of two cubes then​

Correct option is C

Given:

$$\text{Volume of cube: } V = a^3 \\\text{Surface area of cube: } S = 6a^2 \\$$

Formula:

$$\text{Side length } a = V^{1/3}, \quad \text{also } a = \sqrt{S/6} \\$$

Solution:

$$\text{From both, } \frac{V}{S^{3/2}} = \text{constant} \Rightarrow \frac{V_1}{S_1^{3/2}} = \frac{V_2}{S_2^{3/2}} \\\textbf{Final Answer:} \\\ \\\boxed{\frac{v_1}{s_1^{3/2}} = \frac{v_2}{s_2^{3/2}}}$$

$$\frac{v_1}{v_2} = \left( \frac{s_1}{s_2} \right)^{\frac{3}{2}}$$​​