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  3. 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 .
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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 .

Answers (1)
D Deependra Verma

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                2pi rh=pi rl Rightarrow 2h=lRightarrow frachl=frac12Rightarrow h:l=1:2

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