Question

two cylinder have same lateral surface area the ratio of their radii is 3 : 2 find the ratio of their height

Answer 1

Dimensions of one cylinder: r1 and h1Dimensions of second cylinder: r2 and h2
r1:r2 = 3:2
Lateral surface area of first cylinder = lateral surface area of second cylinder
2πr1h1 = 2πr2h2
r1 = h2= 3
_ _ _
r2 h1 2
so, h1 : h2 = 2:3

Answer 2

take radii as 2x and 3x respectively.2 X pi X 2x  X  h1= 2 X pi X 3x X h2
2x X h1= 3x X h2
3x/2x=h1/h2
so the ratio is 3:2