Question

The diameters of $2$ cones are equal. If their slant heights are in the ratio $5:4$, find the ratios of their curved surfaces.

Answer 1

Let $S_1$ be the Curved surface area of $1^{st}$ cone and $S_2$ be the Curved surface area of $2^{nd}$ cone.
Curved Surface Area of a cone$=\pi rl$, where $r$ is the radius of the cone and $l$ is the slant height of the cone.
Ratio of their curved surfaces$=\frac{S_1}{S_2}=\frac{\pi \times r\times l_1}{\pi \times r\times l_2}$

$\frac{S_1}{S_2}=\frac{5}{4}$
$\therefore S_1:S_2=5:4$.