Answer: B
Let the radii of the two solid spheres be \(r_1\) units and \(r_2\) units respectively. According to the given condition, their volumes are in the ratio: \[ \cfrac{4}{3} \pi r_1^3 : \cfrac{4}{3} \pi r_2^3 = 27 : 8 \Rightarrow r_1^3 : r_2^3 = 27 : 8 \Rightarrow r_1 : r_2 = 3 : 2 \Rightarrow \cfrac{r_1}{r_2} = \cfrac{3}{2} \] Now, the ratio of their curved surface areas is: \[ = \cfrac{4\pi r_1^2}{4\pi r_2^2} = \cfrac{r_1^2}{r_2^2} = \left(\cfrac{r_1}{r_2}\right)^2 = \left(\cfrac{3}{2}\right)^2 = \cfrac{9}{4} = 9 : 4 \]
Let the radii of the two solid spheres be \(r_1\) units and \(r_2\) units respectively. According to the given condition, their volumes are in the ratio: \[ \cfrac{4}{3} \pi r_1^3 : \cfrac{4}{3} \pi r_2^3 = 27 : 8 \Rightarrow r_1^3 : r_2^3 = 27 : 8 \Rightarrow r_1 : r_2 = 3 : 2 \Rightarrow \cfrac{r_1}{r_2} = \cfrac{3}{2} \] Now, the ratio of their curved surface areas is: \[ = \cfrac{4\pi r_1^2}{4\pi r_2^2} = \cfrac{r_1^2}{r_2^2} = \left(\cfrac{r_1}{r_2}\right)^2 = \left(\cfrac{3}{2}\right)^2 = \cfrac{9}{4} = 9 : 4 \]