Question

If the radius of a right circular cylinder is doubled and its curved surface area is not changed, then its height must be _________.

Answer 1

Let r be the radius and h be the height of the cylinder.

∴ Curved surface of the cylinder, C₁ = 2$\mathrm{\pi }$rh

Let the height of the new cylinder be H.

Radius of the new cylinder, R = 2r (Given)

∴ Curved surface of the new cylinder, C₂ = 2$\mathrm{\pi }$RH = 2$\mathrm{\pi }$(2r)H

It is given that, the curved surface areas of the new cylinder is not changed.

∴ C₂ = C₁

⇒ 2$\mathrm{\pi }$(2r)H = 2$\mathrm{\pi }$rh

⇒ $H=\frac{h}{2}$

Thus, the height of the new cylinder is half of the height of given cylinder.

If the radius of a right circular cylinder is doubled and its curved surface area is not changed, then its height must be __halved__.