Q4 of 32 Page 250

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.

H


Given that, the lateral surface area of a cylinder is equal to the curved surface area of a cone and their bases are same.


⇒Let r = radius of cylinder = radius of cone, h = height of cylinder and l = slant height of the cone.


And, lateral surface area of cylinder = 2πrh


Also, curved surface area of cone = πrl


⇒2πrh = πrl




⇒ The ratio of the height of the cylinder to the slant height of the cone = 1:2


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