Discussion
If the ratio of volumes of two cones is 2:3 and the ratio of the radii of their bases is 1:2, then the ratio of their heights will be:
Answer: B
The ratio of heights is 8 : 3. The volume of a cone is one third of pi r squared h, so h is proportional to V divided by r squared. With V in the ratio 2 : 3 and r in the ratio 1 : 2, h1 : h2 = (2/1) : (3/4) = 2 : 0.75 = 8 : 3. The ratio 2 : 1 ignores the radius, 3 : 8 is inverted and 3 : 2 uses the volumes only.
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