UPSC 2015 CDS II Math Paper

Let r and h be the original radius and height of the cylinder, respectively
Therefore, initial curved surface area of the cylinder, C = 2πrh
New height of the cylinder = 2h
Therefore, new curved surface area of the cylinder, C′=2πr×2h=2×2πrh=2×
Initial curved surface area of the cylinder.
Hence, statement 1 is correct.
Let r be the original radius of the hemisphere.
Therefore, initial total surface area of the hemisphere,C=3πr2
New radius of the hemisphere = 2r
Therefore, new total surface area ofthe hemisphere
C′=3π(2r)2=4×3πr2=4× Initial total surface area of the hemisphere
Hence, statement 2 is correct.