The volume of a cylinder and cone are in the ratio 3 : 1 with same height. How are their diameters compared?

Diameter of cylinder = diameter of cone

Ratio of volume:

Cylinder :  Cone = \(\pi\)r₁²h   :    \(\frac{1}{3}\) \(\pi\) r₂²h

⇒ 3 r₁²  :   r₂²   =  3 : 1 (given)

Therefore,

⇒ r₁² :  r₂² = 1 : 1

⇒   r₁ :  r₂  = 1 : 1 ⇒  diameters are also equal

So, diameter of cylinder = diameter of cone