The volumes of two cones are in the ratio 1 : 12 and the radii of the cones are in the ratio of 1 : 3. What is the ratio of their heights?
Select the correct option.
A) 3 : 4  B) 2 : 7  C) 2 : 2  D) 2 : 1  E) 2 : 9

Rationale: the volume of the cone = ( 1 / 3 ) π r 2 h only radius ( r ) and height ( h ) are varying . hence , ( 1 / 3 ) π may be ignored . v 1 / v 2 = r 12 h 1 / r 22 h 2 = > 1 / 12 = ( 1 ) 2 h 1 / ( 3 ) 2 h 2 = > h 1 / h 2 = 3 / 4 i . e . h 1 : h 2 = 3 : 4 answer : a
Answer: A