Question

The diameters of the two cones are equal. If their slant heights are in the ratio of $5:4$, find the ratio of their curved surface areas?

Answer 1

Find the ratio of the curved surface areas:

Let us consider the slant height of the two cones be $l_1$ and $l_2$ respectively.

Thus, we have

$l_1:l_2=5:4$

The curved surface area of cone of radius $r$ and slant height $l$ $=\mathrm{\pi rl}$

The curved surface area of the two cones: ${\mathrm{\pi rl}}_1$ and $\mathrm{\pi r}{l}_2$.

We can write the ratio of their curved surface area ​$=\frac{{\mathrm{\pi rl}}_1}{{\mathrm{\pi rl}}_2}$

$\Rightarrow \frac{l_1}{l_2}=\frac{5}{4}$

Since, if the diameters of the two cones are equal then their radius will also remain same.

Hence, the ratio of the curved surface areas is $5:4$.