If the ratio of the volumes of two cylinders is 6 : 1 and the ratio of their heights is 1 : 6, then what is the ratio of their radii ?

9 : 1  3 : 1 8 : 1 6 : 1

6 : 1

Ratio of heights   = 1  :  6 Ratio of volumes = 6  :  1 r₁²h₁  :  r₂²h₂     = 6  :  1 (volume of a cylinder = \(\pi \)r²h) r₁²     :    6r₂²     = 6  :  1 r₁²     :    r₂²       = 36  :  1 r₁  :  r₂  = 6  :  1