Question

The radius of a cylinder is doubled but its lateral surface area is unchanged. Then what must be its height???

Answer 1

lateral surface area of cylinder = 2*π*r*h
 where  r= radius
and        h= height of cylinder

now if lateral surface is same and radius is changed. To compensate the  effect of radius, height will also change

both lateral surface area same but new radius = 2*old radius=2*r

2*π*r*$h_{1}$ =2* (2*r)* $\pi$ * $h_{2}$

2 \pi on both side will get cancelled

[tex]r* h_{1} =2*r* h_{2} [/tex]

now r on both side will get cancelled.

$h_{1} =2*h_{2}$

dividing both side by 2
$\frac{ h_{1} }{2} = \frac{ 2*h_{2} }{2}$

$\frac{h_{1} }{2}= h_{2}$

so new height will be half of old height

Answer 2

Answer is halved......