Question

If the radius of a certain cylinder is doubled and its curved surface area is not changed, then find the ratio of height in two cases.

(a) 1:2
(b) 2:1
(c) 1:4
(d) 4:1

Answer 1

After doubling the radius of a cylinder and keeping the curved surface area unchanged, the ratio of the original height to the new height is 2:1, corresponding to option (b).

Step-by-step explanation:

If the radius of a cylinder is doubled and its curved surface area remains unchanged, we need to find the ratio of the height in two cases.

The formula for the curved surface area of a cylinder is 2πrh, where r is the radius and h is the height of the cylinder. For the initial cylinder, let the curved surface area be A = 2πr₁h₁.

After doubling the radius, the new radius is r₂ = 2r₁, and we want the curved surface area to remain A, so we have A = 2πr₂h₂ = 2π(2r₁)h₂. To keep A the same, we need 2πr₁h₁ = 4πr₁h₂, which simplifies to h₁ = 2h₂.

Thus, the ratio of the height in the two cases is 2:1, which corresponds to option (b).