Answer: A
Let the radii of the two solid spheres be \(r_1\) units and \(r_2\) units, respectively.
∴ According to the condition, their volume ratio is
\(\cfrac{4}{3} πr_1^3 : \cfrac{4}{3} πr_2^3 = 1 : 8\)
Or, \(r_1^3 : r_2^3 = 8 : 27\)
Or, \(r_1 : r_2 = 2 : 3\)
Or, \(\cfrac{r_1}{r_2} = \cfrac{2}{3}\)
Now, the ratio of their curved surface areas is
\(= \cfrac{4πr_1^2}{4πr_2^2 }\) \( = \cfrac{r_1^2}{r_2^2 }\) \( = \left(\cfrac{r_1}{r_2 }\right)^2\)
\( = \left(\cfrac{2}{3}\right)^2\) \( = \cfrac{4}{9} = 4 : 9\)
Let the radii of the two solid spheres be \(r_1\) units and \(r_2\) units, respectively.
∴ According to the condition, their volume ratio is
\(\cfrac{4}{3} πr_1^3 : \cfrac{4}{3} πr_2^3 = 1 : 8\)
Or, \(r_1^3 : r_2^3 = 8 : 27\)
Or, \(r_1 : r_2 = 2 : 3\)
Or, \(\cfrac{r_1}{r_2} = \cfrac{2}{3}\)
Now, the ratio of their curved surface areas is
\(= \cfrac{4πr_1^2}{4πr_2^2 }\) \( = \cfrac{r_1^2}{r_2^2 }\) \( = \left(\cfrac{r_1}{r_2 }\right)^2\)
\( = \left(\cfrac{2}{3}\right)^2\) \( = \cfrac{4}{9} = 4 : 9\)