# The lateral surface of a cylinder is equal to the curved surface of a cone . If the radius be the same , find the ratio of the height of the cylinder and slant height of the cone .

Solution: Let $r$ be the radius of both the cylinder and the cone .

Let $h$ and $l$ respectively be the height and slant height of the cylinder and the cone  . Then ,

Lateral surface of the cylinder = Curface surface of the cone

$\Rightarrow$                $2\pi rh=\pi rl \Rightarrow 2h=l\Rightarrow \frac{h}{l}=\frac{1}{2}\Rightarrow h:l=1:2$

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