Question

if the radius of a cylinder is doubled keeping its lateral surface area the same then what is its height​

Answer 1

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$\bf\large\underline\pink{Solution:-}$

Let the original radius of a cylinder be (r) and original height of a cylinder be (h).

Original lateral surface area of a cylinder= 2π rh

Radius is doubled then new radius is(R)= 2r

New height of a cylinder= H

New lateral surface area of a cylinder= 2π RH

Original lateral surface area of a cylinder= new lateral surface area of a cylinder

[Given : Lateral surface area of both the cylinders are equal]

2πrh= 2πRH

h= 2H

H= h/2

Hence, the height of a new cylinder is Halved of the original cylinder (h/2).

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Answer 2

$\huge\star\mathfrak\blue{{Answer:-}}$

The lateral surface area of a cylinder is A = 2pi rh. Now since the lateral surface area is kept same, 2pi rh = 4 pi rH. Hence H = h/2. Hence the new height is half the original height