If the radius of a cylinder is doubled keeping its lateral surface area the same then its height is...
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Let the initial radius be r. Height be h.
Now, The lateral surface Area is 2
πrh.
The radius is doubled then radius =2r
Let the new height be xh.
Lateral surface is same in both cases.
2πrh = 2π2r(xh)
rh = 2x *rh
2x=1
x = 1/2 .
Therefore ,the new height is h/2 .
Height is halved !
Now, The lateral surface Area is 2
πrh.
The radius is doubled then radius =2r
Let the new height be xh.
Lateral surface is same in both cases.
2πrh = 2π2r(xh)
rh = 2x *rh
2x=1
x = 1/2 .
Therefore ,the new height is h/2 .
Height is halved !
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