Question

The radius and the slant height of a cone are in the ratio $7:13$ and the curved surface area is $286c{m}^2$. Find its radius.

• A. $5cm$
• B. $7cm$
• C. $8.8cm$
• D. $10.3cm$

Answer 1

The correct option is B $7cm$

Given, ratio of radius and slant height $=7:13$.

Let radius, $r=7x$ and slant height, $h=13x$.

Also, curved surface area og the cone $=286c{m}^2$.

But we know, the curved surface area of a cone $=\pi rl$.

Then,
$⟹286=\frac{22}{7}\times 7x\times 13x$
$⟹$ $x^2=\frac{286}{22\times 13}=1$
$⟹x=1$.

$\therefore$ The required radius, $r=7cm$.

Hence, option $B$ is correct.