The radii of two solid cones are equal and their slant heights are in the ratio 7 : 4. The ratio between their curved surface areas is :

1. 4 : 7

2. 7 : 4

3. 16 : 49

4. 49 : 16

Let radii of both the cones be r units each.

Let slant height of two cones be l₁ and l₂.

Curved surface area of first cone = πrl₁

Curved surface area of second cone = πrl₂

$\dfrac{\text{CSA of 1st cone}}{\text{CSA of 2nd cone}} = \dfrac{πrl$1}{πrl2} = \dfrac{l1}{l2} = \dfrac{7}{4} = 7 : 4.

Hence, Option 2 is the correct option.