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Question
If the radius of a cylinder is tripled but its curved surface area is unchanged, then its height will be ______.
Options
tripled
constant
one sixth
one third
Solution
If the radius of a cylinder is tripled but its curved surface area is unchanged, then its height will be one third.
Explanation:
Let h' be the new height.
Curved surface area of a cylinder with radius r and height h = 2πrh
Now, according to the question, radius is tripled. Then,
Curved surface area = 2π × 3r × h' = 2πrh ...[Given]
⇒ 6πr × h' = 2πrh
⇒ `h^' = (2pirh)/(6pir)`
∴ `h^' = 1/3 h`
Hence, the new height will be `1/3` of the original height.
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