If the radius and slant height of a cone are in the ratio 7 : 13 and its curved surface area is 286 cm², find its radius.

We have

Let radius of cone = 7x

Let slant height = 13x

Curved surface area of cone = 286 cm²

= πrl = 286 , 22/7×7x×13x = 286

= x² = 1

= x = 1

Hence radius of cone = 7×1 = 7 cm