Q. 43.7( 27 Votes )
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
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