Question

if the radius of a cylinder is doubled keeping it's lateral surface area the same then what is it height. with steps

Answer 1

So height of cylinder radius 2r =half of height of cylinder of radius r

Answer 2

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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Hope this will help you...