Question

If the radius of a cylinder is doubled keeping Its lateral surface area the same, then what is its height?

Answer 1

Let the initial radius and height of the cylinder be r and h. 

Then L.S.A. = 2πrh 

When r is doubled and the L.S.A. remains the same, then the height be hr By problem new 

L.S.A. = 2πrh 

= 2π (2r) (h₁) 

⇒ 2πrh = 4πrh₁

∴ \(\frac {\pi rh}{4\pi r} = \frac 12h\)

Height becomes its half.