Question

The diameters of two cones are equal. If their slant heights are in the ratio $5:4$, find the ratio of their curved surfaces area.​

Answer 1

Given, diameter of two cones are equal. slant heights are in the ratio $5:4$
We know that radius $=\frac{\text{diameter}}{2}$
$\Rightarrow$ Radii of the two cones are also equal.

Let the slant height of 1st cone be $l_1$ and slant height of 2nd cone can 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 $\frac{\pi r{l}_1}{\pi r{l}_2}$
$=\frac{l_1}{l_2}=5:4[\because \frac{l_1}{l_2}=5:4]$
So, the ratio of curved surface areas is $5:4$