Let the radii of the two solid spheres be \(r_1\) units and \(r_2\) units respectively. ∴ According to the condition, their surface area ratio is \(4πr_1^2 : 4πr_2^2 = 1 : 4\) ⇒ \(r_1^2 : r_2^2 = 1 : 4\) ⇒ \(r_1 : r_2 = 1 : 2\) ⇒ \(\frac{r_1}{r_2} = \frac{1}{2}\) Now, the ratio of their volumes is \(\frac{\frac{4}{3} πr_1^3}{\frac{4}{3} πr_2^3}\) \(= \frac{r_1^3}{r_2^3} = \left(\frac{r_1}{r_2}\right)^3 = \left(\frac{1}{2}\right)^3 = \frac{1}{8} = 1 : 8\)