Question

Two circular cylinders of equal volume have their heights in the ratio 1 : 2 Ratio of their radii is

Options

• \[1 : \sqrt{2}\]

   

• \[\sqrt{2}: 1\]

   

• 1 : 2

• 1 : 4

Answer 1

Let V₁ and V₂ be the volume of the two cylinders with h₁ and h₂ as their heights:

Let r₁ and r₂ be their base radius.

It is given that

`V_1 = V_2 " and "  h_1/h_2 = 1/2`

`pir_1^2 h_1 = pir_22 h_2`

`⇒ (r_1^2)/(r_2^2) = h_2/h_1`

`⇒(r_1^2)/(r_2^2) = 2`

`⇒(r_1)/(r_2) =sqrt(2)/1`