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If the height of a cylinder becomes $14$ of the original height and the radius is doubled, then which of the following will be true.

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Curved surface area of the cylinder will be doubled.

Curved surface area of the cylinder will remain unchanged.

Curved surface area of the cylinder will be halved.

Curved surface area will be

14

of the original curved surface.

answer is C.

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Detailed Solution

We have been given that the height of a cylinder becomes

14

of the original height and the radius is doubled.
Let the original height of the cylinder and radius be h and r respectively and the height and radius of new cylinder be H and R respectively.
Therefore, we have,

H = 14 h and R = 2 r

We know the curved surface area of cylinder with radius r and height h =

2 πrh

.
Then, curved surface of the new cylinder is,

\Rightarrow 2 πRH

⇒2π (2r)

\times \frac{1}{4} h

\Rightarrow 4 πr \times \frac{1}{4} h

\Rightarrow πrh

\Rightarrow \frac{1}{2} \times 2 πrh

\Rightarrow \frac{1}{2} \times

Original curved surface area
Therefore, if the height of a cylinder becomes

14

of the original height and the radius is doubled, then the curved surface area of the cylinder will be halved.
Hence, option (3) is correct.

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