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.

Answer 1

Let $r_1$ and $r_2$ be the radii of the two cones and let the slant height of the first cone be ${}^{\prime }l{.}^{\prime }$

The slant height of the second cone $=2\times$ Slant height of the first cone (Given)

Then, slant height of the second cone $=2l$.

It is given that the curved surface of the first cone $=2\times$ curved surface of the second cone

$\pi r_{1}l=2\times \pi r_2\left(2l\right)$ [$\because$ curved surface of cone $=\pi rl$]

$\Rightarrow \pi r_{1}l=4\pi r_{2}l$

$\Rightarrow r_1=4r_2$

$\Rightarrow \frac{r_1}{r_2}=\frac{4}{1}$

$\therefore$, Ratio of their radii $4:1$.