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.

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