Question

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.

Answer 1

It is given that the curved surface area (C.S.A) of the cone is 286 cm² and that the ratio between the base radius and the slant height is 7: 13. The formula of the curved surface area of a cone with base radius ‘r’ and slant height ‘l’ is given as

Curved Surface Area = πrl

Since only the ratio between the base radius and the slant height is given, we shall use them by introducing a constant ‘k’

So, r = 7k

l = 13k

Substituting the values of C.S.A, base radius, slant height and using `pi 22/7` in the above equation,

Curved Surface Area, 286 = `((22).(7k).(13k))/7`

286 = 286 k²

1 = k²

Hence the value of k = 1

From this we can find the value of base radius,

r = 7k

r = 7

Therefore the base radius of the cone is  7 cm .