The lateral surface area of a cylinder is equal to the curved surface area of a cone. If their bases be the same, find the ratio of the height of the cylinder to the slant height of the cone.

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Solution

Lateral surface area of a cylinder = $2 π r h$
If their bases are same then radius of base will be same
Curved surface area = $π r l$
Now, $π r l = 2 π r h$
$l = 2 h$
$\frac{h}{l} = \frac{1}{2}$

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The lateral surface area of a cylinder is equal to the curved surface area of a cone. If their bases be the same, find the ratio of the height of the cylinder to the slant height of the cone.

Lateral surface area of a cylinder = 2πrh If their bases are same then radius of base will be same Curved surface area = πrl Now, πrl=2πrh l=2h hl=12

Lateral surface area of a cylinder = $2 π r h$
If their bases are same then radius of base will be same
Curved surface area = $π r l$
Now, $π r l = 2 π r h$
$l = 2 h$
$\frac{h}{l} = \frac{1}{2}$