Question

If the ratio of the base radii of two cones having the same curved surface areas is $6:7$, then the ratio of their slant heights is $7:m$. Find $m$.

Answer 1

Let the slant heights of two cones be $l$ and $L$. And their radii be $r$ and $R$.

$\therefore \left(\pi \right)rl=\left(\pi \right)RL$
$\frac{r}{R}=\frac{L}{l}$

$\frac{6}{7}=\frac{L}{l}$

$\therefore l:L=7:6=7:m$
Hence, $m=6$.