The diameters of the bases of two cones are equal. If their slant heights are in the ratio of 3 : 4, then what will the ratio of their curved surface areas be?

Correct option is D

Given:

The diameters of the bases of the two cones are equal.

The slant heights of the two cones are in the ratio 3 : 4

Formula used:

$r$ is the radius of the base,

$l$ is the slant height.

The curved surface area of a cone = πrl

Solution:

Since the diameters of the two cones are equal, their radius will also be the same. 

Let the slant height of the two cones be l₁ and l₂ respectively.

So,  l₁  :   l₂ = 3 : 4

The curved surface area of the two cones is πrl₁ and πr l₂.

So, the ratio of their curved surface area is $$\frac{πrl_1}{πr l_2}$$​​

π and r are canceled.

​$$\frac{l_1}{l_2}= \frac{3}4$$​​

Therefore, the ratio of the curved surface area of two cones is 3 : 4.