Quantitative Aptitude Ques 1280

Question: If the ratio of the volume of two cones is 1: 6 and the ratio of the radii of their bases is 1: 2, then the ratio of their height will be

Options:

A) 2 : 3

B) 3 : 4

C) 1: 3

D) 4 : 9

Show Answer

Answer:

Correct Answer: A

Solution:

  • Let the volume of the cones are $ V _1 $ and $ V _2, $ also’ their radius are $ R _1 $ and $ R _2, $ respectively. Then, according to the question, $ \frac{V _1}{V _2}=\frac{1}{6} $ and $ \frac{R _1}{R _2}=\frac{1}{2} $ Let the height of the cones are $ H _1 $ and $ H _2 $ which are in ratio $ k:1 $

$ \therefore $ $ \frac{H _1}{H _2}=\frac{k}{1} $ Then, $ \frac{\frac{1}{3}\pi R_1^{2}H _1}{\frac{1}{3}\pi R_2^{2}H _2}=\frac{1}{6} $
$ \Rightarrow $ $ {{( \frac{R _1}{R _2} )}^{2}}\times ( \frac{H _1}{H _2} )=\frac{1}{6} $

$ \Rightarrow $ $ {{( \frac{1}{2} )}^{2}}\times \frac{k}{1}=\frac{1}{6} $
$ \Rightarrow $ $ k=\frac{2\times 2}{6}=\frac{2}{3} $

$ \Rightarrow $ $ \frac{H _1}{H _2}=\frac{2/3}{1}=\frac{2}{3} $