Consider the following statements 1 If the height of a cylinder is doubled the area of the curved su...........

Quantitative Aptitude (CDS) Mensuration 3D

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Consider the following statements:

1. If the height of a cylinder is doubled, the area of the curved surface is doubled.

2. If the radius of a hemispherical solid is doubled, its total surface area becomes fourfold.

Which of the above statements is/are correct?

1 only

2 only

Both 1 and 2

Neither 1 nor 2

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Explanation:

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
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.