Answer: Option C
Let their radii be R and r
Then,
$$\eqalign{
& \frac{{\frac{2}{3}\pi {R^3}}}{{\frac{2}{3}\pi {r^3}}} = \frac{{6.4}}{{21.6}} \cr
& \Rightarrow {\left( {\frac{R}{r}} \right)^3} = \frac{8}{{27}} \cr
& \Rightarrow {\left( {\frac{R}{r}} \right)^3} = {\left( {\frac{2}{3}} \right)^3} \cr
& \Rightarrow \frac{R}{r} = \frac{2}{3} \cr} $$
∴ Ratio of curved surface area :
$$ = \frac{{2\pi {R^2}}}{{2\pi {r^2}}} = {\left( {\frac{R}{r}} \right)^2} = \frac{4}{9}\,or\,4:9$$