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Question

Answers

A)$1:3$ B) $1:4$ C) $1:2$ D) $1:5$

Answer
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Given, the lateral surface of a cylinder is equal to the curved surface of a cone. The radius of the cylinder is equal to the radius of the cone. We have to find the ratio of the height of the cylinder and the slant height of the cone. We know that the lateral surface area of cylinder$ = 2\pi {\text{rh}}$where r= the radius of cylinder and h= height of cylinder. Also, the curved surface area of cone$ = \pi {\text{Rl}}$where R=radius of the cone and l- slant height of the cone. Here, given r=R and according to question,

The lateral surface area of a cylinder= the curved surface area of the cone

On putting the given values we get,

$

\Rightarrow 2\pi {\text{rh = }}\pi {\text{rl}} \\

\\

$

On simplifying we get,

$ \Rightarrow \dfrac{{\text{h}}}{{\text{l}}} = \dfrac{{\pi {\text{r}}}}{{2\pi {\text{r}}}} = \dfrac{1}{2}$

Hence the