The curved surface area of one cone is twice that of the other while the slant height of the latter is twice that of the former.

(b) 4 : 1
If the slant height of the first cone is l, then the slant height of the second cone will be 2l.
Let the radii of the first and second cones be r and R, respectively.
Then we have:

$\pi r l=2 \times(\pi R \times 2 l)$

$\Rightarrow r=4 R$

$\Rightarrow \frac{r}{R}=\frac{4}{1}$