Question

two cylinders have same lateral surface area their radii are in the ratio 3:2 find the ratio of their height

Answer 1

$2\pi \: rh = 2\pi \: r1h1$
2*3*h=2*2*h1
H/h1=2/3
H:h1=2:3

Answer 2

Dimensions of one cylinder= r1 and h1
Dimension of second cylinder= r2 and h2
r1,r2=3:2
Lateral surface of first cylinder=lateral surface area of second cylinder

2πr1h1=2πr2h2
r1 / r2 = h2 / h1
So,
Therefore h1 : h2= 2:3