In a cylinder, if radius is doubled and height is halved, curved surface area will be _________.

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Solution

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

∴ Curved surface of the original cylinder, C₁ = 2 $π$ rh

If the radius is doubled and height is halved, then

Radius of the new cylinder, R = 2r

Height of the new cylinder, H = $\frac{h}{2}$

∴ Curved surface of the new cylinder, C₂ = $2 π R H = 2 π \times 2 r \times \frac{h}{2}$ = 2 $π$ rh

Thus, the curved surface area of the new cylinder is same as the curved surface area of the original cylinder.

In a cylinder, if radius is doubled and height is halved, curved surface area will be same.

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