Question

The diameters of two cones are equal. If their slant heights are in the ratio 7:4, then the ratio of their curved surface areas is ________.

• A. 4:7
• B. 49:16
• C. 16:49
• D. 7:4

Answer 1

The correct option is D 7:4

Given: diameters of two cones are equal.
Hence, their radii are also equal.

Given: the slant heights are in the ratio 7:4.
Let the slant heights of the cones be $l_1$ and $l_2$.

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
$=\frac{\pi r{l}_1}{\pi r{l}_2}=\frac{l_1}{l_2}=\frac{7}{4}$

So, the ratio of their curved surface areas is $7:4$.