Question

The diameters of two cones are equal. If their slant heights are in the ratio 5 : 4, find the ratio of their curved surfaces.

Answer 1

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

Now there are two cones with base radius and slant heights as, and, respectively.

Since the base diameters of both the cones are equal we get that = =

Since only the ratio between slant heights of the two cones is given as 5: 4, we shall use them by introducing a constant ‘k’

So, now

= 5k

= 4k

Using these values we shall evaluate the ratio between the curved surface areas of the two cones

=

=

=

Hence the ratio between the curved surface areas of the two cones with the mentioned dimensions is