The volumes of two right circular cylinders have a ratio of 2:3. If the radii of these cylinders are in the ratio of 1:2, what is the ratio of their heights?
Show answer & explanation
Correct answer: D
Explanation
Given:
Ratio of volumes = 2 : 3
Ratio of radii = 1 : 2
By formula:
Volume of cylinder = πr²h
Ratio of volumes = r₁²h₁ : r₂²h₂
r₁ : r₂ = 1 : 2
r₁² : r₂² = 1² : 2² = 1 : 4
r₁²h₁ : r₂²h₂ = 2 : 3
(1 × h₁) : (4 × h₂) = 2 : 3
h₁ : 4h₂ = 2 : 3
h₁ / 4h₂ = 2/3
3h₁ = 8h₂
h₁ : h₂ = 8 : 3
Ratio of heights = 8 : 3