Question

The radius and slant height of a right circular cone are in the ratio of $7:13$ and its curved surface area is ${286cm}^2$.Find its radius $(Use\pi =\frac{22}{7})$.

Answer 1

It is given that the ratio of the radius and the slant height is $7:13$

$\Rightarrow \frac{r}{l}=\frac{7}{13}$

Thus we can assume that

$r=7x$ and $l=13x$

Now, it is given that

$C.S.A=286c{m}^2$

$\Rightarrow \pi rl=286$

$\Rightarrow \frac{22}{7}\times 7x\times 13x=286$

$\Rightarrow 286x^2=286$

$\Rightarrow x^2=1$

$\Rightarrow x=\pm 1$

$\because x\ne -1$

$\therefore x=1$

Now we know that radius

$=7x$

$\Rightarrow 7\left(1\right)=7cm.$