Question

The radii of two right circular cone are in the ratio of $4:5$ and their slant heights are in the ratio $2:3$. Then the ratio of their curved surfaces is:

• A. None of these
• B. $6:17$
• C. $8:15$
• D. $1:1$

Answer 1

Answer: (C)

Given, the ratio of radii is $4:5$ and the ratio of slant height is $2:3$.

Let the radii of two right circular cones is $4x$ and $5x$ and slant height is $2y$ and $3y$.

We know, the curved surface area of the right circular cone $=\pi rl$.

Then, the curved surface area of the first right circular cone $=\pi \times 4x\times 2y=8\pi xy$ sq. cm.

And curved surface area of secondright circular cone $=\pi \times 5x\times 3y=15\pi xy$ sq. cm.

So ratio of CSA of both right circular cone $=8\pi xy:15\pi xy=8:15$.

Hence, option $B$ is correct.