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?

The curved surface area (CSA) of a cylinder is given by the formula:

CSA=2πrh\text{CSA}=2\pi rhCSA=2πrh

where rrr is the radius and hhh is the height of the cylinder. If the radius is increased to twice its original value (r′=2rr'=2rr′=2r) and the height is reduced to half its original value (h′=h2h'=\frac{h}{2}h′=2h​), the new curved surface area becomes:

CSA′=2π(2r)(h2)=2πrh\text{CSA}'=2\pi (2r)\left(\frac{h}{2}\right)=2\pi rhCSA′=2π(2r)(2h​)=2πrh

This is exactly the same as the original curved surface area. Conclusion: The curved surface area of the cylinder remains unchanged when the radius is doubled and the height is halved