Question

two circular cylinders of equal volume have their height in the ratio of 1 : 2 the ratio of their radius is​

Answer 1

answer is in the attachment

which is √2:1

Answer 2

Given :

Two circular cylinders of equal volume have their height in the ratio of 1 : 2 .

To find :

The ratio of their radius.

Solution :

Let the radius of circular cylinders be r₁ and ​r₂

And heights be 1 units and 2 units respectively.

∵ Volume of cylinder = πr²h

So atq,

⇒ πr₁²h = πr₂²h

⇒ r₁² (1) = r₂² (2)      [Cancelling 'π' from both sides]

⇒ r₁² = 2r₂²

⇒ r₁²/r₂² = 2

⇒ √(r₁²/r₂²) = √2     [Square rooting on both sides]

⇒ r₁/r₂ = √2/1

⇒ r₁ : r₂ = √2 : 1

∴ Ratio of their radius = √2 : 1