Question

Two right circular cylinders of equal volumes have their heights in the ratio 1 : 2. The ratio of their radii is ______.

पर्याय

• `sqrt(2) : 1`

• 1 : 2

• 1 : 4

• `1 : sqrt(2)`

Answer 1

Two right circular cylinders of equal volumes have their heights in the ratio 1 : 2. The ratio of their radii is `underlinebb(sqrt(2) : 1)`.

Explanation:

Let first cylinder’s radii = R₁

Height = H₁

Second cylinder radii = R₂

Height = H₂

Ratio of their heights = 1 : 2 (H₁ : H₂)

According to the question,

Volume of first cylinder = Volume of second cylinder

`πR_1^2H_1 = πR_2^2H_2`

Putting the value of H₁ and H₂

⇒ `πR_1^2(1) = πR_2^2(2)`

⇒ `R_1^2 = 2R_2^2`

⇒ `(R_1^2)/(R_2^2) = 2`

⇒ `(R_1/R_2)^2 = (sqrt(2))^2`

⇒ `R_1/R_2 = sqrt(2)/1`

⇒ R₁ : R₂ = `sqrt(2) : 1`