Mathematics
The radius of a cylinder is doubled and its curved surface area is kept as same, the height of the cylinder is:
same
doubled
halved
none of these
Mensuration
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Answer
Let the original radius and height of a cylinder be r and h units, respectively.
Given, radius of the cylinder is doubled.
∴ New radius = 2r
Let H be the new height of the cylinder.
By formula,
Curved surface area = 2π x radius x height
Original curved surface area = 2πrh
New curved surface area = 2π x (2r) x H = 4πrH
Given,
Curved surface area remains same.
⇒ 2πrh = 4πrH
⇒ H = .
Hence, option 3 is the correct option.
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Statement 1: Each side of a cuboid is doubled, its total surface area is also doubled.
Statement 2: The surface area of resulting cuboid is 2 x 2 x 2 times the original area.
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Assertion (A): The radius of a hemisphere increases from r cm to 2r cm. The ratio between the surface area of the original hemisphere and the resulting hemisphere is 1 : 4.
Reason (R): Surface area of the first case = πr2 + 2πr2
Surface area of the second case = π(2r)2 + 2π(2r)2
A is true, but R is false.
A is false, but R is true.
Both A and R are true, and R is the correct reason for A.
Both A and R are true, and R is the incorrect reason for A.