Question

The diameters of two cones are equal. If their slant heights are in the ratio 4:9, then the ratio of their curved surface areas is ________.

• A. 2:3
• B. 3:2
• C. 4:9
• D. 9:4

Answer 1

The correct option is C 4:9

Given, diameters of two cones are equal.
We know that, diameter = $\frac{radius}{2}$
Implies radii of the two cones are also equal
Given, the slant heights are in the ratio 4:9

Let the slant height of 1st cone be $l_1$ and slant height of 2nd cone be $l_2$.

Curved surface area of the first cone $=\pi r{l}_1$
Curved surface area of the second cone
$=\pi r{l}_2$

Now, ratio of their curved surface areas
$=\frac{\pi r{l}_1}{\pi r{l}_2}=\frac{l_1}{l_2}=\frac{4}{9}$

So, the ratio of curved surface areas is $4:9$.