Question

The radius of a cone is $7cm$ and its height is $9cm$. The volume of this cone is equal to lateral surface area of another cone which has same radius. Find the slant height of the cone.

Answer 1

We know that the radius of cone $r=7cm$

and its height $h=9cm$

and let the slant height of the second cone be $=l$ $cm$

Then, according to the question.

Numerically: The lateral surface of the second cone $=$ volume of the first cone

$\Rightarrow \pi rl=\frac{1}{3}\pi r^{2}h$

$\Rightarrow l=\frac{1}{3}rh$

On substituting the values we get,

$l=\frac{1}{3}\times 7\times 9$

$\therefore l=21cm$

Thus the required slant height of the second cone $=21cm$