A cylinder and a right circular cone having the same height also have equal volumes. What is the ratio of the radius of the base of the cylinder to that of the cone?

Correct option is C

Given:

Volume of  cylinder  = Volume of  a right circular cone.
Height of cone = height of cylinder = h (say)

Formula used:

Volume of right circular cone = (1/3) × π × r₁² × h
Volume of right circular cylinder = π × r₂² × h
Solution:

Let the radius of cone = r₁ cm and the radius of cylinder = r₂ cm.
According to the question,
(1/3) × π × r₁² × h = π × r₂² × h
=> r₂² = 3 × r₁²
=> r₂ : r₁² = 3 : 1
=> r₁ : r₂ = √3 : 1
=> r₂ : r₁ = 1 : √3
=> r₂ : r₁ = √3 : 3
Then, the ratio of the radius of the cylinder to that of the cone is √3 : 3.