Question

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

Options

•  4 : 5

• 25 : 16

•  16 : 25

• 5 : 4

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 `r_1` ,`l_1` & `r_2` , `l_2` respectively.

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   `l_1`= 5k

`l_2` = 4k

Since the base diameters of both the cones are equal we get that `r_1` = `r_2` = r

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

`(C.S.A_1)/(C.S.A_2) = (pir_1l_1)/(pi r_2l_2)`

`=(pir(5k))/(pir(4k)`

`=5/4`