Question

The radius and slant height of a cone are in the ratio of 4 : 7. If its curved surface area is 792 cm², find its radius. (Use $\mathrm{\pi }$ = 22/7).

Answer 1

It is given that the curved surface area (C.S.A) of the cone is 792 cm² and that the ratio between the base radius and the slant height is 4: 7. The formula of the curved surface area of a cone with base radius ‘r’ and slant height ‘l’ is given as

Curved Surface Area =

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 = 4k

l = 7k

Substituting the values of C.S.A, base radius, slant height and using in the above equation,

Curved Surface Area,

792 =

792 =

9 =

Hence the value of k = 3.

From this we can find the value of base radius,

r = 4k

r = 12

Therefore the base radius of the cone is.