### Solution:

Curved surface area of the cone, , here, is the radius of the cone, is the curved surface area of the cone and is the slant height of the cone.Let us assume the curved surface of the two cones be and respectively,

The slant height of the two cones are and respectively and the radii of the two cones are and respectively.

Now it is stated that the question as the curved surface area of one cone is twice the other, mathematically it can be written as:

On using the formula for the curved surface area, we get:

Since is common in both the places, it can be canceled and written as:

Now it is given that the slant height of one cone is twice the other which means On substituting it in the equation we get,

On simplifying we get:

Since is common on both the sides, we can cancel them out and write it as:

On taking on the left-hand side we get:

Therefore, using ratios, we get:

Therefore, the ratio between the two radii of the cones is .