Question

If the radius and slant height of a cone are in the ratio $4:7$ and its curved surface area is $792c{m}^2$, then its radius is $(\pi =\frac{22}{7})$.

• A. $10$ cm
• B. $8$ cm
• C. $12$ cm
• D. $9$ cm

Answer 1

Answer: (C)

Given, the ratio of radius and slant height of a cone $=4:7$.

Let the radius of the cone be $4a$ and slant height $=7a$ .

Also given, curved surface area $=792$ $c{m}^2$.

We know, the curved surface area of a cone $=\pi rl$, where $r$ is the radius of the cone and $l$ is the slant height.

Hence, curved surface area of this cone $=\frac{22}{7}\times 4a\times 7a=792$
$\therefore a=3$ cm .

Hence, radius $=4a=12$ cm.

Therefore, option $C$ is correct.