If the volume ratio of two solid spheres is 1:8, the ratio of their curved surface areas will be -

Q.If the volume ratio of two solid spheres is 1:8, the ratio of their curved surface areas will be - (a) 1:2 (b) 2:1 (c) 1:4 (d) 1:16

Answer: C

Let the radii of the two solid spheres be \(r_1\) units and \(r_2\) units.
∴ According to the condition, their volume ratio is
\(\cfrac{4}{3} πr_1^3 : \cfrac{4}{3} πr_2^3 = 1 : 8\)
Or, \(r_1^3 : r_2^3 = 1 : 8\)
Or, \(r_1 : r_2 = 1 : 2\)
Or, \(\cfrac{r_1}{r_2} = \cfrac{1}{2}\)

Now, the ratio of their curved surface areas is
\(= \cfrac{4πr_1^2}{4πr_2^2 }\)
\(= \cfrac{r_1^2}{r_2^2 } = \left(\cfrac{r_1}{r_2}\right)^2 = \left(\cfrac{1}{2}\right)^2 = \cfrac{1}{4} = 1 : 4\)