Question

A cylinder and a cone have equal base and heights if their curved surfaces are in the ratio $8:5$, Show that ratio of radius and their base to their height is $3:4$.

Answer 1

Let the radius and height of cylinder and cone be $r$ and $h$.

Let the slant height of cone be $l$.

We know that,

Curved surfaces areas of cylinder $=2\pi rh$

Curved surfaces of cone $=\pi rl$

Ratio =Curved surfaces ares of cylinder/curved surfaces area of cone=$=\frac{2\pi rh}{\pi rl}=\frac{8}{5}$

$\Rightarrow \frac{r}{h}=\frac{3}{4}$

Hence,

ratio of radius to height is $3:4$