Two circular cylinder of equal volume have their height in the ratio 1: 2. The ratio of their radii is

Given: Two cylinders of equal volume.


Heights of the cylinders are in the ratio 1:2


Volume of cylinder is: πr2h (here r and h are radius and height of the cylinder respectively)


Let V1 be the volume of first cylinder


∴ V1 = π(r1)2h1


Let V2 be the volume of second cylinder


∴ V2 = π(r2)2h2


Here,


V1=V2


⇒ π(r1)2h1 = π(r2)2h2


⇒ (r1)2h1 = (r2)2h2


⇒ (r1)2 : (r2)2 = h2 : h1


⇒ (r1)2 : (r2)2 = 2 : 1


⇒ r1 : r2= √2 :1


∴ ratio of the radii of given cylinders is √2 :1

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