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:

1. 4 : 5

2. 5 : 4

3. 16 : 25

4. 25 : 16

Given, ratio of slant height = 5 : 4

Let slant height of 1st cone be 5a and 2nd cone be 4a cm.

For 1st cone,

⇒ Diameter = d

⇒ Radius = r

⇒ Slant height, l = 5a

For 2nd cone,

⇒ Diameter = D

⇒ Radius = R

⇒ Slant height, L = 4a

Given,

⇒ d = D

∴ r = R

$\Rightarrow \dfrac{\text{CSA of 1st cone}}{\text{CSA of 2nd cone}} = \dfrac{π\text{rl}}{π\text{RL}} \\[1em] = \dfrac{\text{l}}{\text{L}} \\[1em] = \dfrac{5\text{a}}{4\text{a}} \\[1em] = \dfrac{5}{4} \\[1em] = 5 : 4$

Hence, option 2 is the correct option.