what will happen to the curved surface area of a cylinder if its radius is increased to twice the original value and height is reduced to half of the original value?

If the radius is doubled and the height is halved, the curved surface area of the cylinder remains unchanged.

Quick Scoop: What happens to the CSA?

Curved Surface Area (CSA) of a cylinder is given by
CSA=2πrh\text{CSA}=2\pi rhCSA=2πrh.

• Let the original radius be rrr and height be hhh.
  • Original CSA = 2πrh2\pi rh2πrh.

• New radius = 2r2r2r (twice the original).
• New height = h2\dfrac{h}{2}2h​ (half the original).

New CSA:

CSAnew=2π(2r)(h2)=2π⋅2r⋅h2=2πrh\text{CSA}_{\text{new}}=2\pi (2r)\left(\frac{h}{2}\right) =2\pi \cdot 2r\cdot \frac{h}{2} =2\pi rhCSAnew​=2π(2r)(2h​)=2π⋅2r⋅2h​=2πrh

So:

The curved surface area stays the same — it does not increase or decrease.

Intuitive mini-story

Imagine you have a paper label wrapped around a cold drink can.

• If you make the can fatter (bigger radius) but also shorter in just the right way, the total area of that label can stay exactly the same.
• Doubling the radius makes the “wrap” longer around, but halving the height makes it shorter vertically, and these two effects cancel each other out.

So in your exact situation, the “side area” of the cylinder does not change at all.

Answer in one line:
When the radius is doubled and the height is halved, the curved surface area of the cylinder remains unchanged.

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Find out what will happen to the curved surface area of a cylinder if its radius is increased to twice the original value and height is reduced to half of the original value, with an easy formula-based explanation.