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Consider the following statements regarding the cylinder and the hemispherical solid? I. If the height of a cylinder is tripled, curved surface area becomes eight times. II. If the radius of a hemispherical solid is doubled, its total surface area becomes four times.

Consider the following statements regarding the cylinder and the hemispherical solid? I. If the height of a cylinder is tripled, curved surface area becomes eight times. II. If the radius of a hemispherical solid is doubled, its total surface area becomes four times. Correct Answer Only II is correct.

Given:

Height of the cylinder is tripled and, curved surface area becomes eight times.

Radius of the hemisphere is doubled and, total surface area becomes four times.

Concept:

Let 'h' be the height of the cylinder.

Curved surface area of the cylinder = 2πrh

Let 'r'  be the radius of the hemisphere.

Total surface area of the hemisphere = 3πr²

Calculations:

As, h = 3h,

Then its curved surface area = 2πr(3h)

= 6πrh

So, the curved surface area of the cylinder becomes 'six' times.

Statement I is incorrect.

As, r = 2r,

Then its total surface area = 3π(2r)2

= 3π(4r2)

= 4 × (3πr2)

So, the total surface area of the hemisphere becomes 'four' times.

Statement II is correct.

∴ Only statement II is correct. 

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