There are two cones .The curved surface area of one is twice that of the other.
Question:

There are two cones .The curved surface area of one is twice that of the other. The slant height of the later is twice that of the former. Find the ratio of their radii.

Solution:

Let the curved surface area of $1^{5 t}$ cone $=2 x$

C.S.A of $2^{\text {nd }}$ cone $=x$

Slant height of $1^{\text {st }}$ cone $=h$

Slant height of $2^{\text {nd }}$ cone $=2 \mathrm{~h}$

Therefore $\frac{\text { C.S. A of } 1^{\text {st }} \text { cone }}{\text { C. S. A of } 2^{\text {nd }} \text { cone }}$

$=2 x / x$

$\Rightarrow \pi r_{1} l_{1} / \pi r_{2} l_{2}=2 / 1$

$\Rightarrow r_{1} / r_{2}=4 / 1$

Therefore ratio of r1 and r2 is 4:1.