Question

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

Answer 1

Ratio of radius and slant height of the cone=7:13

Let radius (r)=7x and slant height (l)=13x

$\therefore Curvedsurfacearea=\pi rl=\frac{22}{7}\times 7x\times 13x=286\Rightarrow 286x^2=286\Rightarrow x^2=\frac{286}{286}=1\therefore x=\sqrt{1}=1\therefore Radius=7x=7\times 1=7cm$